I usually don't ask the pit for help with homework (or help at all, for that matter ), but I'm a bit stumped here.

64^x=4 I'm trying to find x, and I'm not sure what to do. I've simplified it down to 8^x=2. Then I made it (2^3)^x=2. Then I made it "(the cube root of 2)^x=2" Where can I go from there?

Help is appreciated
Have you not learned how to use logs yet?

take log of both sides

log 64 ^ x = log 4

using log rules

x log 64 = log 4

x = log 64 / log 4

4 * 4 * 4 = 64

4³ = 64

so the cubed root of 64 = 4.

therefore x = 1/3
Last edited by Gaz_m2k5 at Nov 14, 2007,
Nope, we haven't learned them yet.

Thanks. I got the answer in my head, but I think my teacher wants a step-by-step kind of thing.
Last edited by kirbyrocknroll at Nov 14, 2007,
Quote by kirbyrocknroll
Nope, we haven't learned them yet.

Thanks. I got the answer in my head, but I think my teacher wants a step-by-step kind of thing.

Showing your work sucks, dont it

My teacher made me do that and i screwed up more on paper than in my head, although she denied that
ehehe. ignore what i had earlier.

what your teacher is trying to get you to do here, specifically for 64^x = 4, is to get you to realize that they have similar bases.

you can reduce it into 2^6x = 2^2, since 2^6 is 64. since they have similar bases, you can just go straight to 6x = 2, x =1/3.
Last edited by rky at Nov 14, 2007,
Quote by rky
ehehe. ignore what i had earlier.

what your teacher is trying to get you to do here, specifically for 64^x = 4, is to get you to realize that they have similar bases.

you can reduce it into 2^6x = 2^2, since 2^6 is 64. since they have similar bases, you can just go straight to 6x = 2, x =1/3.

yup.
"And after all of this, I am amazed...

...that I am cursed far more than I am praised."
Quote by rky
ehehe. ignore what i had earlier.

what your teacher is trying to get you to do here, specifically for 64^x = 4, is to get you to realize that they have similar bases.

you can reduce it into 2^6x = 2^2, since 2^6 is 64. since they have similar bases, you can just go straight to 6x = 2, x =1/3.

Thank you.