Question

How do I solve this equation: 2^(4x) = 9^(x-1) for x?

Answer 1

@satellite73 do you know how I can solve this?

Answer 2

start with
\[4x\ln(2)=(x-1)\ln(9)\] and then do some algebra

Answer 3

I got up to: 4x = (x-1)log9/log2

Answer 4

do I have to use natural log?

Answer 5

Does not matter. Same answer.

Answer 6

don't forget \(\ln(2)\) and \(\ln(9)\) are just numbers (constants) so treat them as such
no you can use any log you like, but you only have two on your calculator

Answer 7

but how would I solve this equation with log?

Answer 8

think of them as \(a\) and \(b\)

Answer 9

Okay... I guess I will let sattelite handle it :P .

Answer 10

alright

Answer 11

\[4x\ln(2)=(x-1)\ln(9)\]
\[4x\ln(2)=x\ln(9)-\ln(9)\]
\[4\ln(2)x-\ln(9)x=-\ln(9)\]
\[(4\ln(2)-\ln(9))x=-\ln(9)\]
\[x=\frac{-\ln(9)}{4\ln(2)-\ln(9)}\] it is algebra all the way, and you should check my work because my algebra is lousy