I have been watching your video's for a week now, I am amazed how they are bringing back to me what I learned at school. I left school in 1969, when I went to college to study engineering together with an apprenticeship. There were no calculators in those days they began to appear during the last year or two of my four year engineering course. Much later I got funding from my company to study an engineering degree part time. Nowhere in my career did i ever need to use more than basic math because i was managing work rather than doing it myself, you can forget a lot of math if you do not use it. A week ago I wouldn't have remembered how to use logs to do this but I succeeded in getting the right answer today before I watched your video. I expect we did it at school, but we had to use log tables. I think at my age it is important to have something to do to keep the old grey cells in good order. Regarding something you said in another video relating to how some children might not get on well with their teacher, I put myself in that category for the first three years at senior school. Not that my teacher wasn't a nice man, but I just couldn't understand his strong Polish accent, I also missed a lot of school because I had Asthma and got more than my fair share of childhood illness like Glandular fever, Scarlet fever and several others. It is very difficult for a child to catch up when they have time off school for illness, especially when they are not understanding their teacher. I didn't really realise I could do mathematics until I went into the fourth year, we had a different teacher, a man with enthusiasm like you. I went from being in the bottom three of the class to being in the top three. I am enjoying re learning some of this and once i have ensured i remember all the basics i might get the math book out I used at University and brush up on that, I never studied all of it anyway, only the sections relevant to the courses I did like Structures and Hydraulics and Drainage.
There were and I had two, but they were only good for a rough calculation say to at best within a tenth of a millimetre or more or checking the. Much of the math I did early in my career required the use of seven figure logarithms to get accuracy of three decimal places in mm or four in inches @@daintree98
Hello John, I really enjoy all the videos, more importantly the explanation that you offer. Furthermore, the emphasis on *common sense* rather than on mathematics is amazing. I am 68 now. Whenever I watch the videos, old memories of my student life fly in. The videos make me reasonable to say that mathematical procedures now have changed a lot - what used to be taught during our student era has completely changed. Great John! God bless you!
Thanks for what you do! I was following my dream of owning my own fab shop and was working on a degree in mechanical engineering which I wanted to get a masters in, when we deployed to a really unhappy place. Said place is where I got blown up twice in under 4 hours. Significant brain injury, as in not fun. My sports car v12 brain now runs on 3 cyl and is out of its timing. Your videos help Mr to remember I used to be able to do stuff like this even though I’ll forget it all in a half an hour. No sympathies sought no sadness desired, I’m a blessed person, and I enjoy your videos
WOW! Not bad. I 5-second-calc'ed -.67, as it looked as if it s/b about -2/3rds. As always...another great lesson. Keep 'em coming prof. I'm 71 & I feel as if I'm back in HS in Brooklyn, NY. (In a good way)
…when we find ourselves at your stage, here, we then need to first go back a stage or page or more then work our way back up to this level of math. Won’t take but a day or two or more…. If we don’t know or have forgotten how to do multiplication and division we won’t understand how to do fractions, for the most part. In which case, we must first refresh ourselves or learn multiplication and division before we can understand and do fractions.
Greetings. The answer is X = -.613 rounded. The value for X is determined as follows 6^X+2 =12 can be rewritten as 6^X time 6^2 = 12, consequently the expression is 6^X = 1/3 and Log 6^X =Log 1/3. Moving on, we get X Log 6 = Log 1/3 and Log 1/3 = -.47712, Log 6 = .77815, dividing -47712 by .77815 gives -.61315. When this value for X is added to 2 we get 1.38685. That means that 6^1.38685 =12 and or approximately equivalent to 12. We get 11.99994. That is close enough, don't you think?
you can also get the same answer by applying log6 to both sides, netting x + 2 = log6(12) = 1.386852807 (rounded). -2 to both sides, and you get x = -0.613147193 (rounded)
So, I did this in about 10 seconds in my head (except taking the log, which I did with a table of logarithms -- couldn't find my log-log slide rule, that took almost another 30 seconds to do), and did it by factoring out a 6 from both sides, to get 6ˣ⁺¹=2; then, I took the log of both sides, and continued with (x+1)log 6 = log 2. x + 1 = log(2)/log(6), and finally x = (log(2)/log(6)) - 1, which gives -0.613 to three decimal places.
@@louise7552 But what about that part of his audience who doesn’t know how to do it without algebra like you…? What about those who are new to logarithmic and exponential functions and equations, unlike yourself, but like you yourself once were too…?
x = -log(3) / log(6) Should NOT take a competent teacher nearly 16 minutes to explain just PART of this! Also it would be helpful to point out that the base of the logarithms is irrelevant.
At 6:48 you said "It's gonna have to be a negative value less than 1". A "negative value less than 1" would be any negative value, which would not be correct. I think it would be clearer to say "It's gonna have to be a negative value greater than -1". Or maybe "It's gonna have to be a value greater than -1 and less than 0". (My interpretation of what you said is based on how computer programming logic works, because that is my career background. In that world, -1000 is less than -100, which is less than -1, which is less than 0, which is less than 1)
The Tutor can just go straight to the question as if solving it with Y11 students which majority won’t even get their heads around it. But the way this Tutor goes about his solution, a Y4 Pupil who knows well his/her four rules, ie + - x /, would be able to understand the Problem. Mathematics is NOT an easy fix but a following of Procedure. And that is the reason why most students DO NOT do well in Maths. They don’t want to follow simple instructions but want things their way. The Tutor knows what he is about and what he wants to achieve. Wise up
Many don’t get this type of problem till Algebra 2 I didn’t get this in Algebra 1 back in 1973- 1974..and in my day we didn’t have calculators we did have tables at the back of the book.
We could use calculators for home work, but not tests or quizzes. And you had to show what you did, so you were screwed if you didn't know how to do it the long way... I didn't have a calculator because my father didn't want me using one, so it was always the long way for me. 😁
Same here! No calculators. I think it was around this level of algebra that I determined that it made no practical sense and I would never need it in my life. I was right.
Any problem involving compound interest would use exponential equations like this one. For example if you invest $1000 at 3% interest compounded continuously and 5 years later a friend invests $1000 at 4% interest compounded continuously when will your friend's investment be worth more than yours?
The digression about all the different kinds of equations is totally superfluous and unnecessary confusing. Talking about all the things a problem is not just adds a whole lot of information people don't need to know to solve the problem. THey will learn the differences through experience. It it jsut a whole lot easier to learn things as you deal with them than dealing with things in the abstract when they don'' t actually related to the problem at hand. Analogy: In learning a foreign language, you present the word that you're learning, you don't present 5 or six other words you're not learning in that lesson and then say, don't worry about those now. You should focus on what needs to be learned, not all all the stuff that isn't relevant to the problem at hand. Frankly, you seem to have the "grad student syndrome", where it's more important to you to show your students how much you know than it is to teach them the lesson at hand. Your ego is showing, and it's not pretty.
I was way off on my approach to this one, though my result was in the "reasonable" range. I was thinking you could take the 6th root of both sides and wind up with X+2 = 12^1/6, X=-0.4869.. It's been way too long since I've worked problems like this.
Same comment as one of the other comments. Manipulate the expression to obtain 6^x = 1/3 before taking the log. Makes the remainder of the problem simpler to solve. Plus it's good practice working with exponents.
Why not start by seeing that 6^(x+2) = 12 => 6^x * 6^2 = 12 ; so 6^x = 12/36 =1/3. then taking logs both sides x log 6 = log (1/3) => x = log (1/3) / log 6? then use calculator. I get -0.613147. Hmm. Now I look, I see this is a popular approach!
I love math. for the sake of math. But I have to agree...when, in the real world, would a problem like this arrive? Engineering? certainly not in counting cows or weighing produce.
The only problem I have with the last part of the solution is that we don't need to divide "both sides" of the equation by Log 6. If we have (X + 2) times Log 6 = Log 12 we divide Log 12 by Log 6 which will equals (X + 2). And then we proceed to substract 2 from our result to find "X". In other words it seems unnecessary to say that we need to divide "both sides" and somewhat confusing. Ex: If X times 2 = 8 we only need to divide 8 by 2 to find X. I don't see the point of dividing 2 by 2. Ex2: If 4 + X = 12 we don't need to substract 4 from 4. We only need to substract 4 from 12 and we get "X". The same goes for multiplication and division. So why adding a layer when it's not needed. That's my question at the end of the day. A common sense question but maybe I am missing something. But very instructive video nonetheless as you refreshed my memory about Logarithms. But I am not ready yet for Mr Sine et lady Cosine. :)
What you do to one side of an equation you must do to the other side. Otherwise it wouldn’t be an equation and statement of truth. I’m more than willing to bet that he goes about the last part in the same shorter and quicker manner that you point out here when he solves this type of equation and other types of equations for himself alone. Like you, in doing it only for himself, he wouldn’t waste time doing it like he does here! So you must patiently understand that his main point here is to show those new and perhaps rusty to this stuff, the people he’s really aiming at and teaching, how to solve equations for x in the step by step fashion seen here so as to give them a justification for doing it the way even you do it once they reach your level of intuition and understanding of the subject after having been provided with clarity and understanding of the process and peace of mind in process because by they’ll then know that they’re justified in doing it your way. His method is mainly aimed at those people, not so much at you! For instance, and perhaps emphasis, What would the student new to algebra and solving equations do with 0.17x = 100 if the teacher said to them, “solve for x by clearing decimals,” but the student didn’t know the rule which states that they’re supposed to do to one side of an equation the same thing they do to the other side? Would the student new to the game know that 17x = 10,000 if they knew nothing about treating both sides of the equation equally? Would they know that in clearing the decimal 0.17 to 17 they must also multiply the other side of the equation by 100 to keep the equation balanced and true! So that’s what the teacher is teaching and doing here… you’re just taking the shortcut, sort of speak, the quicker implied way, the intuitive way, if you will. What you’re talking about is for those like yourself who already know the rule…!
@@ndailorw5079 Thanks for your comment but I finally understood the method and I agree with you. I am now working on it to improve my algebra. Since I made this comment I got the point as I said in more recent remarks.
@@aryusure1943 Well… in all fairness to you, you did post your comment 2 months ago, after all. Good to see and know you’ve had a change of heart and mind and still plugging away since then. And I applaud your sincerity and honesty, no offense intended… not that I’m anybody special, of course. It’s just that mathematics is a sequential step by step foundational and an exact and a precise game, for the most part. What we learn is if built from and upon what we’ve learn prerequisite to what we’re now learning. If it’s essentials and fundamentals are taught in a sloppy and negligent manner results will be faulty and incorrect, not to even mention sloppy, to boot. Again, I know immediately in my head, and for times sake, that 2x - 3 + y = 5x + 6 goes immediately to y = 3x + 9 without literally doing to one side of the equation what I did to the other side in step by step fashion, but the student new to algebra needs an explanation and thereby a justification for doing so and doing it so quickly and easily. There’s no peace of mind with the new student when they must just simply accept that as truth without understanding the why of it all, never mind the how, just now! Imagine accepting something that in your heart of hearts you really don’t understand! Once the new student learn the why, then do it your way! So, I get upset when people who know all I’ve said and therefore should know why the instructor goes about things the way he does here rails against him as though they themselves have known this stuff since birth without having had the need of first being taught that you must do to one side of an equation what you do to the other side in order to keep both sides of the equation equal and true at every instance, is all! That’s why they call it an equation, it’s a symbol of perfect balance at each and every step! If I take 5 pounds off this side of a balanced scale and that side rises while the other side lowers, I must then remove 5 pounds from the other and lower side of the balanced scale to bring it back to a state of equilibrium and balance, and truth…. Same thing in solving equations… some of us are now just capable of doing in our heads instead of on the blackboard.. or paper.. like you! I know… a lot of wind… pardon me…?
@@ndailorw5079 No worries! We are finally in agreement. And trust me I have a lot to learn (or "relearn"). As I was saying in my original comment "maybe I was missing something". Now, I know. Cheers!
@@aryusure1943 Likewise. And best of luck to you! And no doubt you’ll master every “step” of the way while building step upon step as you go on your way to mastering not merely some particular mathematical subject or topic, but the whole of the field of mathematics, as much as you choose to, that is. Can’t miss, seeing your humbleness and humility and your openness to constructive criticism. At least, that’s if we could consider and call my particular brand of long-winded round-about vitriol constructive criticism….? But, again, you’ll both be and do just fine, and will be up and running again in no time at all. Once we learn the essential fundamentals that underlie mathematics and that tie it all together, and learn all its rules, and put in some well reasoned thought, mathematics becomes easy… because then, it does itself, pretty much! Cart before the horse (at every step!), in other and shorter words. The great scientific and mathematical philosophers and discovers who laid it all out were, and still are, for those among us now, the true geniuses. But we little people, lol, excepting the exceptions, and for the most part, are simply following their lead; all we’ve got to do is pay close and strict attention! But we all have a bright light go off in our heads from time to time, too, no doubt! Oh well… if there was any offense at all, even in the least, my apologies. Cheers!
…these as well as other logarithmic and exponential functions and equations are used to solve many real-life problems. They’re used in banking and finance and at home to calculate compounded interest over a certain time range, they used to calculate house or car depreciation; exponential growth, used to determine the growth of a population over a period of time; used to determine exponential decay, many things decay exponentially, radioactive substances, some chemicals during certain reactions, air pressure as a function of altitude, etc., for examples.
Your answer of x = log 12/log 6 - 2 is not simplified. I did log 12 = log 2 + log 6 to make x = (log 2 + log 6)/log 6 - 2 and then x = log 2/log 6 - 1 and then x = log 2/(log 2 + log 3) - 1. Everyone should know that log 2 = 0.3010 and log 3 = 0.4771 or the answer is x = 0.3010/(.3010 + 0.4771) - 1 = -0.6132 As an engineer, it is assumed that you know those logs just like the square root of 2 is 1.414
…but then it seems to me that your being an engineer should most certainly remind you that you weren’t always an engineer, and were certainly not born one… he’s not teaching to engineers here, he’s teaching to the newly indoctrinated, for the most part, and to the somewhat rusty, or the frozen stuck rusty…. You yourself even had to first learn the rudiments and essentials of mathematics before you started sending rockets to Jupiter, or measuring the weight of the earth, or designing foundations for super tall skyscrapers, etc… You’re talking speed! He’s teaching the uninitiated the how to before they themselves through practice and perhaps with his assistance learn the speed part. His target audience are those who are relatively and comparatively new to this stuff. In other words, give them a chance, and let them first get to that point and level you’ve long since risen above…. Many here are new at this stuff at least at this level in the game, they’re not engineered like you.. yet…
@@ndailorw5079 I learned logs in algebra one when I was in 9th grade at the age of 13. I was not an engineer then but I did pass algebra one. What were you doing at the age of 13? This is very simple math that you should already know how to do.
True and who's life is affected by an unknown exponent? You log yourself until you die exhausted and solve the number of atoms in the universe and not solve a real life problem. Playing with imaginary numbers are as real as winning video games.
…maybe you’re starting at the wrong end of math…? Or maybe you haven’t yet grasped the concepts and rules of exponential and logarithmic functions and equations. How did you go about it? Others can help out, perhaps, on the matter.
It's meaningless to only teach to this level of understanding...do this and dummy gets a treat. To understand math one needs to know what the calculator is programmed to do. Stuff like this is why curious people hate public schooling and why they are forced to teach themselves about things. I wonder how many more successful people there would be if a proper foundations were laid and a great fertilizer was used.
@@gorillaau Bingo! …then comes the 3 minutes! The instructor is teaching to those who are new to the subject, or weak in it, not to those who already know. But somehow… many of the comments here just don’t get that, or refuses to get it. But you’d think that they did get it, given how adept and fast they appear to be in arriving at their answers. Surely if you can cipher that fast you’re smart enough and fast enough to figure out why the guy takes the time to “work through” the problem at the speed, pace, and manner by which he does! Although, I must say, there are areas, here and there, where it wouldn’t hurt at all if he’d trim a little fat off his approach, method, and manner….?
I have been watching your video's for a week now, I am amazed how they are bringing back to me what I learned at school. I left school in 1969, when I went to college to study engineering together with an apprenticeship. There were no calculators in those days they began to appear during the last year or two of my four year engineering course. Much later I got funding from my company to study an engineering degree part time. Nowhere in my career did i ever need to use more than basic math because i was managing work rather than doing it myself, you can forget a lot of math if you do not use it.
A week ago I wouldn't have remembered how to use logs to do this but I succeeded in getting the right answer today before I watched your video. I expect we did it at school, but we had to use log tables.
I think at my age it is important to have something to do to keep the old grey cells in good order.
Regarding something you said in another video relating to how some children might not get on well with their teacher, I put myself in that category for the first three years at senior school. Not that my teacher wasn't a nice man, but I just couldn't understand his strong Polish accent, I also missed a lot of school because I had Asthma and got more than my fair share of childhood illness like Glandular fever, Scarlet fever and several others. It is very difficult for a child to catch up when they have time off school for illness, especially when they are not understanding their teacher. I didn't really realise I could do mathematics until I went into the fourth year, we had a different teacher, a man with enthusiasm like you. I went from being in the bottom three of the class to being in the top three.
I am enjoying re learning some of this and once i have ensured i remember all the basics i might get the math book out I used at University and brush up on that, I never studied all of it anyway, only the sections relevant to the courses I did like Structures and Hydraulics and Drainage.
Before computerized handheld calculators, there were Slide Rulers.
There were and I had two, but they were only good for a rough calculation say to at best within a tenth of a millimetre or more or checking the. Much of the math I did early in my career required the use of seven figure logarithms to get accuracy of three decimal places in mm or four in inches @@daintree98
Hello John, I really enjoy all the videos, more importantly the explanation that you offer. Furthermore, the emphasis on *common sense* rather than on mathematics is amazing. I am 68 now. Whenever I watch the videos, old memories of my student life fly in. The videos make me reasonable to say that mathematical procedures now have changed a lot - what used to be taught during our student era has completely changed. Great John! God bless you!
Thanks!
Thanks for what you do! I was following my dream of owning my own fab shop and was working on a degree in mechanical engineering which I wanted to get a masters in, when we deployed to a really unhappy place. Said place is where I got blown up twice in under 4 hours.
Significant brain injury, as in not fun. My sports car v12 brain now runs on 3 cyl and is out of its timing.
Your videos help Mr to remember I used to be able to do stuff like this even though I’ll forget it all in a half an hour. No sympathies sought no sadness desired, I’m a blessed person, and I enjoy your videos
Skip to 10:15 and he finally starts to do the problem.
WOW! Not bad. I 5-second-calc'ed -.67, as it looked as if it s/b about -2/3rds.
As always...another great lesson. Keep 'em coming prof. I'm 71 & I feel as if I'm back in HS in Brooklyn, NY.
(In a good way)
Mr. Math Man: You are correct. I have absolutely no idea what to do.
…when we find ourselves at your stage, here, we then need to first go back a stage or page or more then work our way back up to this level of math. Won’t take but a day or two or more…. If we don’t know or have forgotten how to do multiplication and division we won’t understand how to do fractions, for the most part. In which case, we must first refresh ourselves or learn multiplication and division before we can understand and do fractions.
He wastes a hell of a lot of time
@@rogergriffiths3345 He certainly does. Takes 15 minutes to explain and do what should have taken only two!!
Greetings. The answer is X = -.613 rounded. The value for X is determined as follows 6^X+2 =12 can be rewritten as 6^X time 6^2 = 12, consequently the expression is 6^X = 1/3 and Log 6^X =Log 1/3. Moving on, we get X Log 6 = Log 1/3 and Log 1/3 = -.47712, Log 6 = .77815, dividing -47712 by
.77815 gives -.61315. When this value for X is added to 2 we get 1.38685. That means that 6^1.38685 =12 and or approximately equivalent to 12. We get 11.99994. That is close enough, don't you think?
you can also get the same answer by applying log6 to both sides, netting x + 2 = log6(12) = 1.386852807 (rounded). -2 to both sides, and you get x = -0.613147193 (rounded)
So, I did this in about 10 seconds in my head (except taking the log, which I did with a table of logarithms -- couldn't find my log-log slide rule, that took almost another 30 seconds to do), and did it by factoring out a 6 from both sides, to get 6ˣ⁺¹=2; then, I took the log of both sides, and continued with (x+1)log 6 = log 2. x + 1 = log(2)/log(6), and finally x = (log(2)/log(6)) - 1, which gives -0.613 to three decimal places.
0:10 how does a couple of minutes turn into 15 in your world?
Because he's a control freak. I've worked that out without using Algebra.😊
@@louise7552
But what about that part of his audience who doesn’t know how to do it without algebra like you…? What about those who are new to logarithmic and exponential functions and equations, unlike yourself, but like you yourself once were too…?
Before I take the log, I'd change 6^(x+2) = 36 * (6^x) =12.
6^x = 12/36 = 1/3
x = log(1/3)/log6
That's how I did it. It'd be awesome if he showed different ways to get the same solution.
x = -log(3) / log(6)
Should NOT take a competent teacher nearly 16 minutes to explain just PART of this!
Also it would be helpful to point out that the base of the logarithms is irrelevant.
@@DavidLee-qe3rd I like how this teacher goes extremely slowly. Viewers can always transition to someone faster like Black Pen Red Pen.
This one is still a little over my head but I'm getting there. Thanks.
Is math just making things up until it works, regardless if it's right?
At 6:48 you said "It's gonna have to be a negative value less than 1". A "negative value less than 1" would be any negative value, which would not be correct. I think it would be clearer to say "It's gonna have to be a negative value greater than -1". Or maybe "It's gonna have to be a value greater than -1 and less than 0". (My interpretation of what you said is based on how computer programming logic works, because that is my career background. In that world, -1000 is less than -100, which is less than -1, which is less than 0, which is less than 1)
Great. I had forgotten all of this. Simple. Easy.
The Tutor can just go straight to the question as if solving it with Y11 students which majority won’t even get their heads around it. But the way this Tutor goes about his solution, a Y4 Pupil who knows well his/her four rules, ie + - x /, would be able to understand the Problem. Mathematics is NOT an easy fix but a following of Procedure. And that is the reason why most students DO NOT do well in Maths. They don’t want to follow simple instructions but want things their way. The Tutor knows what he is about and what he wants to achieve. Wise up
just curious could you simplify the equation to 6 to the x plus 6 to the 2 = 12. .....since they have the same base ,can you just add the exponents
The equation can be written as 6 to the x TIMES 6 to the 2 = 12.
@@discobear5752 Yes, you could rewrite as:
(6^x) * (6^2) = 12
6^x = 12/(6^2)
6^x = 12/36
6^x = 0.333..
x* log 6 = log 0.333..
x= log 0.333,,/log6
I did it John's way.
Many don’t get this type of problem till Algebra 2 I didn’t get this in Algebra 1 back in 1973- 1974..and in my day we didn’t have calculators we did have tables at the back of the book.
(X+2) = log(12) base 6
(x+2)=log(12)base 6
Log(2 ×6)
Log base 6 of 6 +log base 6 of 2
1 + log(2) base 6
x = l + log(2) base 6 -2
X= (1 + .3869)-2
In high school we did not have calculators, I used a slide rule.
We didn't even have that, all we had was Log tables and trigonometry identities etc
Me too.
reading the comments, i'm thinking noone in this man's audience is under 60
Thank you! THAT MADE SENSE!!! ❤
I would love it if you just explained how to solve the equation without all the fluff
I love you Mr. Math
And to think that when I was in highschool we did not have calculators but logarithm books.
We could use calculators for home work, but not tests or quizzes. And you had to show what you did, so you were screwed if you didn't know how to do it the long way... I didn't have a calculator because my father didn't want me using one, so it was always the long way for me. 😁
Same here, John.
I used tables of logs, because I didn't have a decent slide rule back then. I do now.
Same here! No calculators. I think it was around this level of algebra that I determined that it made no practical sense and I would never need it in my life. I was right.
Please share what a real life example of this equation might be, thanks.
He is teaching you how to solve algebraic equations. If you think this has no real world applications then please enjoy your life in a cave
Any problem involving compound interest would use exponential equations like this one. For example if you invest $1000 at 3% interest compounded continuously and 5 years later a friend invests $1000 at 4% interest compounded continuously when will your friend's investment be worth more than yours?
These eguations are just puzzles or an they represent a solution to a real problem. Please provide examples, thanks, John
I could solve it.thanks alot❤
The digression about all the different kinds of equations is totally superfluous and unnecessary confusing. Talking about all the things a problem is not just adds a whole lot of information people don't need to know to solve the problem. THey will learn the differences through experience. It it jsut a whole lot easier to learn things as you deal with them than dealing with things in the abstract when they don'' t actually related to the problem at hand.
Analogy: In learning a foreign language, you present the word that you're learning, you don't present 5 or six other words you're not learning in that lesson and then say, don't worry about those now. You should focus on what needs to be learned, not all all the stuff that isn't relevant to the problem at hand.
Frankly, you seem to have the "grad student syndrome", where it's more important to you to show your students how much you know than it is to teach them the lesson at hand. Your ego is showing, and it's not pretty.
I was way off on my approach to this one, though my result was in the "reasonable" range. I was thinking you could take the 6th root of both sides and wind up with X+2 = 12^1/6, X=-0.4869.. It's been way too long since I've worked problems like this.
.....log6(12)-2
I feel like I'm a genius 😎
Solved this just using Mobile calci that too without using log......
Just like you I found 6^x=12 and subtracted it with 2
Same comment as one of the other comments. Manipulate the expression to obtain 6^x = 1/3 before taking the log. Makes the remainder of the problem simpler to solve. Plus it's good practice working with exponents.
Thank you! I just start college i never taking a algebra class my 1st class is algebra1105c.
Good video
Why not start by seeing that 6^(x+2) = 12 => 6^x * 6^2 = 12 ; so 6^x = 12/36 =1/3. then taking logs both sides x log 6 = log (1/3) => x = log (1/3) / log 6? then use calculator. I get -0.613147.
Hmm. Now I look, I see this is a popular approach!
(x+2)log6=log12. Once you understand exponential equations you can properly arrange the elements on sight.
I love math. for the sake of math. But I have to agree...when, in the real world, would a problem like this arrive? Engineering? certainly not in counting cows or weighing produce.
I understand the Riemann Hypothesis and elliptic curves but couldn't do this problem. Is it my age. I took algebra in 1964.
Got it! But with trial and errors and my calculator. :(
Now I will learn how to do it by the rules of the trade. :)
x + 2 = log 12/log 6...?
6 power x equal 1/3,then x.ln6 equal -ln3,x equal -ln 3 divided by ln 6 looks more simple
6^x+2 = 12
log 6^x+2 = log 12
(x + 2) log 6
x + 2 = log 12 / log 6
x + 2 -2 = log 12 / log 6 - 2
x = log 12/log 6 -2
x ~ -0.613
X+2 Log 6 = Log 12
X+2 = Log 12 / Log 6
X = (Log 12 / Log 6) -2
At this point I don't have a calculator handy so I'm done.
Also x = ln1/3 divided by ln6 = -0.61314
You don’t talk so much I actually I love when you talk, and the answer is 613
I thought it bad to be negative and that x + 2 was greater than 1. 6 to the power of 1 is 6. 6 squared is 36.
When I went to school we didn't even know what a calculator was then the only phone we ever had was landline
This answer to this problem is x+2 log 6/10 = 12 log/10 =1.2.
X+2x-2og6+6-=12+12_= 1.2 4 24
i would guess x = about -0.5
Seems simple enough with a calculator now that you've explained it to me. However, I'd like to understand where this might be found.
Algebra and beyond.
1.8
Log 12/log 6, then minus 2
I am glad I found a teacher who explains in watermelon seed way
I did the math in my head, and I got: x = (ln(12)/ln(6))-2
LET'S GOOOO I WAS RIGHT GG
The only problem I have with the last part of the solution is that we don't need to divide "both sides" of the equation by Log 6.
If we have (X + 2) times Log 6 = Log 12 we divide Log 12 by Log 6 which will equals (X + 2). And then we proceed to substract 2 from our result to find "X".
In other words it seems unnecessary to say that we need to divide "both sides" and somewhat confusing.
Ex: If X times 2 = 8 we only need to divide 8 by 2 to find X.
I don't see the point of dividing 2 by 2.
Ex2: If 4 + X = 12 we don't need to substract 4 from 4. We only need to substract 4 from 12 and we get "X".
The same goes for multiplication and division.
So why adding a layer when it's not needed. That's my question at the end of the day.
A common sense question but maybe I am missing something.
But very instructive video nonetheless as you refreshed my memory about Logarithms. But I am not ready yet for Mr Sine et lady Cosine. :)
What you do to one side of an equation you must do to the other side. Otherwise it wouldn’t be an equation and statement of truth. I’m more than willing to bet that he goes about the last part in the same shorter and quicker manner that you point out here when he solves this type of equation and other types of equations for himself alone. Like you, in doing it only for himself, he wouldn’t waste time doing it like he does here! So you must patiently understand that his main point here is to show those new and perhaps rusty to this stuff, the people he’s really aiming at and teaching, how to solve equations for x in the step by step fashion seen here so as to give them a justification for doing it the way even you do it once they reach your level of intuition and understanding of the subject after having been provided with clarity and understanding of the process and peace of mind in process because by they’ll then know that they’re justified in doing it your way. His method is mainly aimed at those people, not so much at you! For instance, and perhaps emphasis, What would the student new to algebra and solving equations do with 0.17x = 100 if the teacher said to them, “solve for x by clearing decimals,” but the student didn’t know the rule which states that they’re supposed to do to one side of an equation the same thing they do to the other side? Would the student new to the game know that 17x = 10,000 if they knew nothing about treating both sides of the equation equally? Would they know that in clearing the decimal 0.17 to 17 they must also multiply the other side of the equation by 100 to keep the equation balanced and true! So that’s what the teacher is teaching and doing here… you’re just taking the shortcut, sort of speak, the quicker implied way, the intuitive way, if you will. What you’re talking about is for those like yourself who already know the rule…!
@@ndailorw5079 Thanks for your comment but I finally understood the method and I agree with you.
I am now working on it to improve my algebra.
Since I made this comment I got the point as I said in more recent remarks.
@@aryusure1943
Well… in all fairness to you, you did post your comment 2 months ago, after all. Good to see and know you’ve had a change of heart and mind and still plugging away since then. And I applaud your sincerity and honesty, no offense intended… not that I’m anybody special, of course. It’s just that mathematics is a sequential step by step foundational and an exact and a precise game, for the most part. What we learn is if built from and upon what we’ve learn prerequisite to what we’re now learning. If it’s essentials and fundamentals are taught in a sloppy and negligent manner results will be faulty and incorrect, not to even mention sloppy, to boot. Again, I know immediately in my head, and for times sake, that 2x - 3 + y = 5x + 6 goes immediately to y = 3x + 9 without literally doing to one side of the equation what I did to the other side in step by step fashion, but the student new to algebra needs an explanation and thereby a justification for doing so and doing it so quickly and easily. There’s no peace of mind with the new student when they must just simply accept that as truth without understanding the why of it all, never mind the how, just now! Imagine accepting something that in your heart of hearts you really don’t understand! Once the new student learn the why, then do it your way!
So, I get upset when people who know all I’ve said and therefore should know why the instructor goes about things the way he does here rails against him as though they themselves have known this stuff since birth without having had the need of first being taught that you must do to one side of an equation what you do to the other side in order to keep both sides of the equation equal and true at every instance, is all! That’s why they call it an equation, it’s a symbol of perfect balance at each and every step! If I take 5 pounds off this side of a balanced scale and that side rises while the other side lowers, I must then remove 5 pounds from the other and lower side of the balanced scale to bring it back to a state of equilibrium and balance, and truth…. Same thing in solving equations… some of us are now just capable of doing in our heads instead of on the blackboard.. or paper.. like you!
I know… a lot of wind… pardon me…?
@@ndailorw5079 No worries! We are finally in agreement. And trust me I have a lot to learn (or "relearn"). As I was saying in my original comment "maybe I was missing something". Now, I know.
Cheers!
@@aryusure1943
Likewise. And best of luck to you! And no doubt you’ll master every “step” of the way while building step upon step as you go on your way to mastering not merely some particular mathematical subject or topic, but the whole of the field of mathematics, as much as you choose to, that is. Can’t miss, seeing your humbleness and humility and your openness to constructive criticism. At least, that’s if we could consider and call my particular brand of long-winded round-about vitriol constructive criticism….? But, again, you’ll both be and do just fine, and will be up and running again in no time at all. Once we learn the essential fundamentals that underlie mathematics and that tie it all together, and learn all its rules, and put in some well reasoned thought, mathematics becomes easy… because then, it does itself, pretty much! Cart before the horse (at every step!), in other and shorter words. The great scientific and mathematical philosophers and discovers who laid it all out were, and still are, for those among us now, the true geniuses. But we little people, lol, excepting the exceptions, and for the most part, are simply following their lead; all we’ve got to do is pay close and strict attention! But we all have a bright light go off in our heads from time to time, too, no doubt!
Oh well… if there was any offense at all, even in the least, my apologies. Cheers!
I would just say x = ln12/ln6 - 2
…but how did you get to that point?
x = log4
I get it but I still don’t understand Logrithms!
…yeah, but what exactly are you asking, what don’t you understand about logarithms, or, whadda you mean by, “…I still don’t understand logarithms”?
All I knew was that you had to use logs. That’s it.
When will you ever use this equation? What job do you need it for?
…these as well as other logarithmic and exponential functions and equations are used to solve many real-life problems. They’re used in banking and finance and at home to calculate compounded interest over a certain time range, they used to calculate house or car depreciation; exponential growth, used to determine the growth of a population over a period of time; used to determine exponential decay, many things decay exponentially, radioactive substances, some chemicals during certain reactions, air pressure as a function of altitude, etc., for examples.
6(1).2 = 622
Your answer of x = log 12/log 6 - 2 is not simplified. I did log 12 = log 2 + log 6 to make x = (log 2 + log 6)/log 6 - 2 and then x = log 2/log 6 - 1 and then x = log 2/(log 2 + log 3) - 1. Everyone should know that log 2 = 0.3010 and log 3 = 0.4771 or the answer is x = 0.3010/(.3010 + 0.4771) - 1 = -0.6132 As an engineer, it is assumed that you know those logs just like the square root of 2 is 1.414
…but then it seems to me that your being an engineer should most certainly remind you that you weren’t always an engineer, and were certainly not born one… he’s not teaching to engineers here, he’s teaching to the newly indoctrinated, for the most part, and to the somewhat rusty, or the frozen stuck rusty…. You yourself even had to first learn the rudiments and essentials of mathematics before you started sending rockets to Jupiter, or measuring the weight of the earth, or designing foundations for super tall skyscrapers, etc… You’re talking speed! He’s teaching the uninitiated the how to before they themselves through practice and perhaps with his assistance learn the speed part. His target audience are those who are relatively and comparatively new to this stuff.
In other words, give them a chance, and let them first get to that point and level you’ve long since risen above…. Many here are new at this stuff at least at this level in the game, they’re not engineered like you.. yet…
@@ndailorw5079 I learned logs in algebra one when I was in 9th grade at the age of 13. I was not an engineer then but I did pass algebra one. What were you doing at the age of 13? This is very simple math that you should already know how to do.
12 = 6*2...that fact should have used in the solution
@davidhockley1082
…and.. then what..?
-1
-.61
613
I used the calculator for the last step: - log 3 / log 6... and let the reader figure out why. 😅
Hint: 6^(x+2) = 6^x * 6^2
Second hint: 12/ 36 = 1/3
Third hint: 1/3 = 3^-1
Half of the solution is looking at the adds.
X=1
Solve the question without use of log tables Otherwise this is a one min question
I wish you would just get to the problem and not talk so much. I just give up and go on to a.other subject. I never finish.
Just speed up the playback to 2X.....
I know aaahhhh
Like reading, doing math takes time and patience. The world really isn't TikTok moments.
The youth these days. Geez
@@mski435well, I'm 70 and I find these videos long winded.
Is it zero
True and who's life is affected by an unknown exponent? You log yourself until you die exhausted and solve the number of atoms in the universe and not solve a real life problem. Playing with imaginary numbers are as real as winning video games.
Nothing easy about this, I came out 0.00000, stuff is unlearnable!😊
…maybe you’re starting at the wrong end of math…? Or maybe you haven’t yet grasped the concepts and rules of exponential and logarithmic functions and equations. How did you go about it? Others can help out, perhaps, on the matter.
It's meaningless to only teach to this level of understanding...do this and dummy gets a treat. To understand math one needs to know what the calculator is programmed to do. Stuff like this is why curious people hate public schooling and why they are forced to teach themselves about things. I wonder how many more successful people there would be if a proper foundations were laid and a great fertilizer was used.
No clue at all.
…then you’ve missed something at the previous and earlier stages and levels of mathematics, after that, the rest is easy, relatively speaking…
Don't waste time talking in the beginning
Solution is way too wordy. Do in 3 minutes or less please.
In mathematics, the understanding and the working out is more important than the answer.
This is not about mathematics. This is about teaching method. @@gorillaau
@@gorillaau
Bingo! …then comes the 3 minutes! The instructor is teaching to those who are new to the subject, or weak in it, not to those who already know. But somehow… many of the comments here just don’t get that, or refuses to get it. But you’d think that they did get it, given how adept and fast they appear to be in arriving at their answers. Surely if you can cipher that fast you’re smart enough and fast enough to figure out why the guy takes the time to “work through” the problem at the speed, pace, and manner by which he does! Although, I must say, there are areas, here and there, where it wouldn’t hurt at all if he’d trim a little fat off his approach, method, and manner….?
Too much BS to subscribe
Make it short. You spend lot of time unnecessarily
Your lectures are too long.³
Why is math like Chinese? Good Lord!
…maybe because you have to learn the language first…?🫤
When I start understanding, I find their is to much useless talking before going back to solving.
(X+2) = log(12) base 6
(x+2)=log(12)base 6
Log(2 ×6)
Log base 6 of 6 +log base 6 of 2
1 + log(2) base 6
x = l + log(2) base 6 -2
X= (1 + .3869)-2