Log(Base5)3 = x Another way of writing this is 5^x = 3 Take log(Base10) of both sides Log(5^x) = Log(3) xLog(5) = Log(3) Answer = Log(3)/Log(5) ≈ .48/.70 ≈ .68
@Charlie-wt7ct Yes, less than 1. But the option 3/5 is also less than 1... and, as it happens, only 0.08 away from the correct answer. It was only because I believed this was an option because the problem itself used both 3 and 5 that I dismissed this option.
You can pick the correct answer without a calculator. Log₅3 = x Therefore 5ˣ = 3 Lets try using 0.68 as the exponent but turn it into the fraction 2/3 as this is 0.66 in decimals. ⅔ So, 5 = 3 This means that we square 5 and then find the cube root of the result to see if it's close to three. 5 squared is 25 which is close to 27 and the cube root of 27 is 3. So 0.68 is slightly larger than 2/3 and is the closest answer out of the four that are given.
With multiple choice it was easy. I knew that 5^0=1 and 5^1=5, so the answer has to be between 0 and 1, because 3 is between 1 and 5. But I wanted to know why. I have forgotten a lot of my high school Algebra 2, but I feel pretty sure that we were never taught about this "change of base formula." Thanks, John, for demonstrating it.
I keep seeing slide rule comments. This is the kind of problem for which you would have used a table of logarithms. Yeah, you might do the division on a slide rule, whereas a log-log slide rule might be a bit more far off. If you really want, use a table for everything, including the log(log) part [to speed up the division]. Abbreviated Trig and Log Tables could be found in many high school math textbooks. I used them extensively in school. Yeah, slide rule, too, for banging out some chem homework, even.
We can substitute the result I'm this manner. 5^1 is 5 and 5^2 is 25. But, we have to derive the of x to arrive at 3. Therefore the value of x should be less than 1. In the mca ( multi choice answer), the value less than 1 is 0.68. Therefore, x is 0.68.
@@argonwheatbelly63799.9% of people on earth have no clue how to use a slide rule! You have be *taught* how to use a slide. I have cashiers that don't know how to make change from $1 Bill without help from the cash register.
Yes, another 'advantage' back in pre-70's was that stuff tended to be 'over-engineered' by virtue of having maybe 10% 'wiggle room' to make up for inherent inaccuracies of SRs. Of course, logarithm tables (and maybe mainframe computers) were the final arbiter, albeit a lengthy one. Stuff generally tended to be tougher, heavier back then to allow for the 'unknowns'.
Immediately I can see that the only possible answers are 3/5 and 0.68, so I sensed a trap and guessed it had to be 0.68. Checking it in my head without a calculator is a bit of a chore but showed I was right. I remember that log2 = 0.30, this means log8 = 0.90 and log 80 = 1.90. I then reason that log 9 (sq rt 81) must be a bit more than 0.95 and log 3 (sq rt 9) is just under 0.48. log 5 = 0.70 (because 0.30 + 0l70 = 1.00). 4.8/7 = 0.6857 ... Apart from the calculation I have just explained, I cannot see a short cut using a slide rule.
log from 3 to the base of 5 is... ...b) 3/5. and you can rule out solution a and d on the spot... ..but it cannot be c neither, since already 5tothepowerofminus2 is 1/25 and remains the fraction b ) 3/5... and thinking of 5tothepowerof0 is 1 and fivetothepowerof1 is 5, you need - to get 3 - something in between tothepowerof0 and tothepowerof1... ...remains b as 5/5 is 1 and 1/ 5 is 0,2. so it is well in between 0 and 1... ...right? Le p'tit Daniel
I would suggest you modify how you teach log and ln subjects. This video is filled with to much dialogue for such a simple subject. My recomendation would be to have a video entitled "Solving Logarithmic Problems" AND a separate video entitled "Solving Natural Lograthmic Problems" where you present examples of both much like the subect of this VERY lengthy video.
Log(Base5)3 = x
Another way of writing this is
5^x = 3
Take log(Base10) of both sides
Log(5^x) = Log(3)
xLog(5) = Log(3)
Answer = Log(3)/Log(5) ≈ .48/.70 ≈ .68
@Charlie-wt7ct Yes, less than 1. But the option 3/5 is also less than 1... and, as it happens, only 0.08 away from the correct answer. It was only because I believed this was an option because the problem itself used both 3 and 5 that I dismissed this option.
You can pick the correct answer without a calculator.
Log₅3 = x
Therefore 5ˣ = 3
Lets try using 0.68 as the exponent but turn it into the fraction 2/3 as this is 0.66 in decimals.
⅔
So, 5 = 3
This means that we square 5 and then find the cube root of the result to see if it's close to three.
5 squared is 25 which is close to 27 and the cube root of 27 is 3.
So 0.68 is slightly larger than 2/3 and is the closest answer out of the four that are given.
With multiple choice it was easy. I knew that 5^0=1 and 5^1=5, so the answer has to be between 0 and 1, because 3 is between 1 and 5. But I wanted to know why. I have forgotten a lot of my high school Algebra 2, but I feel pretty sure that we were never taught about this "change of base formula." Thanks, John, for demonstrating it.
I keep seeing slide rule comments. This is the kind of problem for which you would have used a table of logarithms. Yeah, you might do the division on a slide rule, whereas a log-log slide rule might be a bit more far off. If you really want, use a table for everything, including the log(log) part [to speed up the division].
Abbreviated Trig and Log Tables could be found in many high school math textbooks. I used them extensively in school. Yeah, slide rule, too, for banging out some chem homework, even.
7:43 It is very easy: you are Looking for solution of 5^x = 3
It must be a number 0,5
We can substitute the result I'm this manner. 5^1 is 5 and 5^2 is 25. But, we have to derive the of x to arrive at 3. Therefore the value of x should be less than 1. In the mca ( multi choice answer), the value less than 1 is 0.68. Therefore, x is 0.68.
Once the change of base formula is memorized, takes only seconds on the Casio fx115ES.
Slide rule are difficult to use, but you had to think back in the 60s. Great tool.
Not difficult. You just need to become familiar with them.
@@argonwheatbelly63799.9% of people on earth have no clue how to use a slide rule! You have be *taught* how to use a slide. I have cashiers that don't know how to make change from $1 Bill without help from the cash register.
0.68260619 approx, so d) is your closest answer, and b) isn't far away
When somebody makes a comment about slide rules, I tell them that the SR-71 was designed by a bunch of guys with slide rules and pocket protectors.
Yes, another 'advantage' back in pre-70's was that stuff tended to be 'over-engineered' by virtue of having maybe 10% 'wiggle room' to make up for inherent inaccuracies of SRs. Of course, logarithm tables (and maybe mainframe computers) were the final arbiter, albeit a lengthy one. Stuff generally tended to be tougher, heavier back then to allow for the 'unknowns'.
Still used slide rules in the 70s, although pocket (shirt pocket) calculators started to become available.
Sometimes you make my 76 y.o. brain hurt..... but that's a good thing.
You had books with log to base 5? Mine had log 10 and 'e'. Otherwise it's the long way around.
Immediately I can see that the only possible answers are 3/5 and 0.68, so I sensed a trap and guessed it had to be 0.68. Checking it in my head without a calculator is a bit of a chore but showed I was right. I remember that log2 = 0.30, this means log8 = 0.90 and log 80 = 1.90. I then reason that log 9 (sq rt 81) must be a bit more than 0.95 and log 3 (sq rt 9) is just under 0.48. log 5 = 0.70 (because 0.30 + 0l70 = 1.00). 4.8/7 = 0.6857 ...
Apart from the calculation I have just explained, I cannot see a short cut using a slide rule.
Thanks
The Windows calculator does have a way of using base 5
Click on the 2nd (top left )
Input 3 log.x (enter 5 in this case)
= 0.68260....
Log(Base5)3 = Y
This is 5^Y= 3
then 0 < Y
What’s the name of the software you using to write please…I would want to use it for my online class
Its smsller than 1 but 3/5 is a trap because it contains the numbers 3 and 5. Log5(3) has noting to do with fraction 3/5.
5^x = 3
xlog5 = log3
x = log3/log5
D) .68
0.68 (D) 0.4771/0.6989
nice!
13:57 But it must be the same base for the denominator as the numerator...right?
Correct.
You could have rounded this off, by explaining that 5^0.68…=3.(!)
log from 3 to the base of 5 is... ...b) 3/5.
and you can rule out solution a and d on the spot... ..but it cannot be c neither, since already 5tothepowerofminus2 is 1/25 and remains the fraction b ) 3/5... and thinking of 5tothepowerof0 is 1 and fivetothepowerof1 is 5, you need - to get 3 - something in between tothepowerof0 and tothepowerof1... ...remains b as 5/5 is 1 and 1/ 5 is 0,2. so it is well in between 0 and 1... ...right?
Le p'tit Daniel
2.1
3/5
log3/log5 or ln3/ln5
B)
Cube root of 27 is 3, so about 2/3 (or cube root of 5 squared), so d
I would suggest you modify how you teach log and ln subjects.
This video is filled with to much dialogue for such a simple subject.
My recomendation would be to have a video entitled "Solving Logarithmic Problems" AND a separate video entitled "Solving Natural Lograthmic Problems" where you present examples of both much like the subect of this VERY lengthy video.
Isn’t there only one possible answer. The distractors are kinda obvious. ln3/ln5 is the answer. It is positive, less than one and not 3/5.
I DON'T GET IT. 3/5 =.6
So 5 to power .6
= 2.6265......
which is not 3
Talk less
But he gets paid by the word! 😊
It must be tough trying to teach math to the woke, and D.E.I. victims 🙂