Question

How do you solve for x?: `2log_3(x) = 3 log_3(4)`

Answer 1

I found `x=8`

Explanation:

We can use a rule of the log to write:
`log_3(x^color(red)(2))=log_3(4^color(red)(3))`

then take `3` to the power of the right and left side to cancel the logs:
`color(blue)(3)^(log_3(x^color(red)(2)))=color(blue)(3)^(log_3(4^color(red)(3)))`
`cancel(color(blue)(3))^(cancel(log_3)(x^color(red)(2)))=cancel(color(blue)(3))^(cancel(log_3)(4^color(red)(3)))`
and get:
`x^2=4^3=64`
`x=+-sqrt(64)=+-8`
we can use only the positive one `x=8`.