Maybe this video is rather a support for beginners? In this case, I think that the person wanted to explain the decomposition of the powers to find out "common factors" ...
17 minutes? For all intents and purposes, it was finished at the 3 minute mark: 8^(x - 1) = 48 or dividing both sides by 8, 8^(x - 2) = 6. Since 8 = 2³, 2^(3x - 6) = 2 × 3. Dividing both sides by 2 again, 2^(3x - 7) = 3. Take logs of both sides ⇒ (3x - 7)log2 = log3, which can be simplified to x =( (log3/log2) +7 )/3. If you've memorized a few base-10 logs, log2 = 0.301, log3 = 0.477 and you're done. All the extraneous manipulations of logarithms is a waste of time.
I don't know why but your way feels like it takes longer to me. Here is how I solved it. 8^x×8-8^x/8=3024 8^x(8-1/8)=3024 8^x(63/8)=3024 8^x=3024×8/63 8^x=384 ln(8^x)=ln(384) x×ln(8)=ln(384) x=ln(384)/ln(8) x=~2.86
@rumpeldrump the same way squares aren't the same as polygons. All squares are polygons but not all polygons are squares. All arithmetic is mathematics but not all mathematics is arithmetic.
@@rumpeldrump Everyone knows it's a blueberry because oranges don't have doors. What does any of that have to do with definitions? Yes describing irrational numbers like the square root of 2 with the √ is more precise than the decimal form, that has absolutely nothing to do with the definition of mathematics or arithmetic? Mathematics is defined as: the abstract science of number, quantity, and space. Arithmetic is defined as: the branch of mathematics dealing with the properties and manipulation of numbers. Arithmetic is a kind of maths.
I don't know why people think turning succinct logs into a bunch of fractions that still have logs in them is simpler. Why introduce potential arithmetic errors in "simplifying" a log, when the calculator does not care at all and works just as well either way.
I'm glad you explained that 1= -1+2, I would have never figured that out
That kind of detail is excruciating,😮
Maybe this video is rather a support for beginners? In this case, I think that the person wanted to explain the decomposition of the powers to find out "common factors" ...
17 minutes? For all intents and purposes, it was finished at the 3 minute mark: 8^(x - 1) = 48 or dividing both sides by 8, 8^(x - 2) = 6. Since 8 = 2³, 2^(3x - 6) = 2 × 3. Dividing both sides by 2 again, 2^(3x - 7) = 3. Take logs of both sides ⇒ (3x - 7)log2 = log3, which can be simplified to x =( (log3/log2) +7 )/3. If you've memorized a few base-10 logs, log2 = 0.301, log3 = 0.477 and you're done. All the extraneous manipulations of logarithms is a waste of time.
You're right ✅️
Agree
Dude explained how 2×2×2=8, but didn't show how he got 48 from dividing 3024 by 63
In this case movie will be more than hour
I don't know why but your way feels like it takes longer to me. Here is how I solved it.
8^x×8-8^x/8=3024
8^x(8-1/8)=3024
8^x(63/8)=3024
8^x=3024×8/63
8^x=384
ln(8^x)=ln(384)
x×ln(8)=ln(384)
x=ln(384)/ln(8)
x=~2.86
Mathematics is not the same as arithmetic.
@rumpeldrump the same way squares aren't the same as polygons.
All squares are polygons but not all polygons are squares.
All arithmetic is mathematics but not all mathematics is arithmetic.
@@jacobcombs1106 I don't see it that way. sqrt(2) is precise, 1.4142 is not 17/12 either.
@@rumpeldrump Everyone knows it's a blueberry because oranges don't have doors.
What does any of that have to do with definitions? Yes describing irrational numbers like the square root of 2 with the √ is more precise than the decimal form, that has absolutely nothing to do with the definition of mathematics or arithmetic?
Mathematics is defined as:
the abstract science of number, quantity, and space.
Arithmetic is defined as:
the branch of mathematics dealing with the properties and manipulation of numbers.
Arithmetic is a kind of maths.
@jacobcombs1106 you talk a lot and say nothing, yes and arithmetic is a sub-area but not precise. everything you say is nonsense.
I generally don’t reduce further once I get to a logA/logB equation. Let the calculator do its job.
It’s was a good refresher for me.
I don't know why people think turning succinct logs into a bunch of fractions that still have logs in them is simpler. Why introduce potential arithmetic errors in "simplifying" a log, when the calculator does not care at all and works just as well either way.
Put off multiplying small factors to get a large number that you’re only going to factor later. Smaller factors are easier to work with.
Good job bro!
😮😮 good
I find that you are always doing complex way.
Sensacional !!!
8^(x+1) - 8^(x-1) = 3024
=> 8^x * 8 - 8^x * (1/8) = 3024
=> 8^x (8 - 1/8) = 3024
=> 8^x (63/8) = 3024
=> 8^x = 3024/(63/8)
=> 8^x = (3024 * 8) / 63
=> 8^x = (3024/9 * 8) / 7
=> 8^x = (1008/3 * 8) / 7
=> 8^x = (336/7) * 8
=> 8^x = 48 * 8
=> 8^x = 6 * 8 * 8
=> 8^(x-2) = 6
=> (x-2).ln(8) = ln(6)
=> x-2 = ln(6)/ln(8)
=> x = log_8(6) + 2
No fractions in this solution:
8^(x+1) - 8^(x-1) = 3024
8^(x-1+2) - 8^(x-1) = 3024
8^(x-1)*8^2 - 8^(x-1) = 3024
8^(x-1)*64 - 8^(x-1)*1 = 3024
8^(x-1)*(64 - 1) = 3024
8^(x-1)*63 = 3024
8^(x-1)*63/63 = 3024/63
8^(x-1) = 48
log(8^[x-1]) = log(48)
(x-1)*log(8) = log(48)
(x-1)*log(8) = log(6*8)
(x-1)*log(8) = log(6) + log(8)
(x-1)*log(8)/log(8) = (log[6] + log[8]) / log(8)
x - 1 = log(6)/log(8) + log(8)/log(8)
x - 1 = log_8(6) + 1
x - 1 + 1 = log_8(6) + 1 + 1
x = log_8(6) + 2
Excellent teacher! Thank you!!!
y = 8^x
8y - y/8 = 3024 = 8(3)(2)(63)
63y = 8(8)(3)(2)(63)
y = 8(8)(3)(2) = 3(2^7) = 8^x = 2^(3x)
2^(3x - 7) = 3
3x - 7 = (log3)/(log2)
x = 7/3 + (log3)/(3log2)
8^x *8 - 8^x/8 = 16*3*63
8^x = 384
X = ln 384 / ln 8 ; X = 2,86
8^(x+1) - 8^(x-1) = 3024
8^x*(8-1/8) = 3024
8^x*(63/8) = 3024
8^x*(3^2*7/2^3) = 2^4*3^3*7
8^x = 2^7*3
(2^3)^ x= 2^7*3
2^(3x) =2^7*3
2^(3x-7) = 3
3x-7 = log_2(3)
x = (7 +log_2(3))/3
8^(x+1) - 8^(x-1) = 3024 || *8
8^(x+2) - 8^x = 3024*8
(8^x)*(8^2 - 1) = 3024*8 || ÷63
8^x = 48*8 || factorize
2^(3*x) = 2^7*3 || log
3*x*log2 = 7*log2 + log3 || ÷log2
3*x = 7 + log3 / log2 || ÷3
and change log base to 2
x = (7 + log[2]3) / 3
X= 2.86...
Everybody has a calculator... so at stage x-1=log48/log8 --> x=1+log48/log8 = 1+1.862 = 2.862 ✅️
Very imprecise.
Avec cette manie de changer de base, on ne sait toujours pas que vaut la réponse !
How does it take 17 minutes to do 8^x(8-1/8), divide both sides by (8-1/8) and do a log operation??
This is not an Olympiad question. Don’t waste people’s time with such simple questions and unnecessarily long solutions!
trivial
17 mins!!!
Common factor 8^x then u are done...
8^x(8-1/8)=3024
8^x=3024/(63/8)
8^x=3024*8/63
x=log_8(3024*8/63)
Mathematical manoeuvring but what is the purpose?
I'm horrified that this is (supposedly) a math Olympiad question
I very much doubt it to be Olympiad standard, its a slightly dressed up log question, 4th form/yr10 roughly, maybe 1 grade higher if I am generous.
waste of time
Maths olympiad and someone is winding and unnecessarily long
B/s 😂
That is not how to properly write an 8.
Can’t you just make the bases of 8 the same and the power is like 378 so x + 1 x - 1 is equal to 8 to the power of 378