Question

3(log)²(base8)x = log(base2) x

Please help me!

Answer 1

\[3\log _{8} x = \log _{2} x \]

Answer 2

I know one answer is 2. I need to know the other roots so I can sum them

Answer 3

Another root is x=1

Answer 4

Omg thank you so much!!!

Answer 5

Hey wait, even x=8 is another. and x=64 is also one. There's something wrong with the question. Infinite values of x are possible!

Answer 6

Oh no!! I had the options 9, 7, 0 and 3. I guessed it was 3

Answer 7

Actually, the thing you posted is an identity. It is always true, for all value of x.

Answer 8

That's weird...

Answer 9

Both 9 and 3 seem right, then.

Answer 10

Dont worry, its not your fault. Are they asking for the sum of the roots?

Answer 11

\[3\log_8x=\log_2x\]\[3\frac{\log_2x}{\log_28}=\log_2x\]\[\frac33\log_2x=\log_2x\]\[\log_2x=\log_2x\]so yeah, identity...

Answer 12

Yes, Mani... It was an important exam for me

Answer 13

Thanks TuringTest!

Answer 14

I get x= 8 and x=1
assuming log^2 for the left hand side

Answer 15

Hey wait, if your question was: \[3(\log_{8}x)^{2}=\log_{2}x \]. Then the answer is possible. By seeing this you can say x=1 is a solution
\[3\log_{8}x \times \log_{8}x=\log_{2}x \]
\[3/3\log_{2}x \times \log_{8} x=\log_{2}x \]
\[\log_{8}x=1 \]
Which means x=8 is a solution
So, answer is 9. I m sorry that u guessed 3 in the exam, but you've to learn from your mistakes

Answer 16

Oh :/ But 2 is also a root, right? Why can't the sum be 3 then?

Answer 17

No, if you put x=2. you get 1/3 on one side, and 1on the other. Was it your final exam?

Answer 18

Is \[(\log _{8} x )^{2}\] the same as \[\log ^{2}_{8} x \] ?

Answer 19

No, it wasn't

Answer 20

Yeah, it is same. But the first one is more generally used

Answer 21

I wish they'd use the first one, that confused me :/

Answer 22

\[ 3 log_8(x) log_8(x)= log_2 x \]

Answer 23

The second use is used for trigonometric functions. Come on, it was just one question!

Answer 24

Well, theres another I didn't know... they asked for the sum of (x²+3x-3)^50 coefficients. I looked it up on wolfram, it's a huge number, how was I suppose to do that?

Answer 25

That requires use of the binomial theorem. In which grade are u?

Answer 26

last one. I kinda know binomial theorem, but even though it's a huuuuge number!

Answer 27

Well, I will have to work on that. I will inform u as soon as I am able to do it

Answer 28

Ok thanks. I appreciate that.

Answer 29

sum of coeffs of (x²+3x-3)^50
This uses a trick. If we sub in x=1, this has the effect of add up the coeffs
here (1+3-3)= 1
and 1^50 = 1

Answer 30

Wow, I'd never thought of that... Tricky indeed. Thanks a lot, phi!

Answer 31

Can we do that with any value of x?

Answer 32

I never thought of it either...but through the magic of the internet, it becomes easy!