Question

How do you solve `4^x=sqrt(5^(x+2))`?

Answer 1

`x = (2log(5))/(4log(2)-log(5))`

Explanation:

Squaring both sides

`4^(2x)=5^2 5^x` or
`16^x=5^x 5^2` or
`(16/5)^x=5^2` now applying `log` to both sidexs
`x(log(16)-log(5))=2log(5)` then
`x = (2log(5))/(4log(2)-log(5))`