Question

What is the inverse of `y = log_2(x^2)` ?

Answer 1

`color(white)(xx)f^-1(x)=2^(x/2)`

Explanation:

`color(white)(xx)y=log_2(x^2)`

The logarithm of the second power of a number is twice the logarithm of the number itself:

`=>y=color(red)2log_2x`
`=>color(red)(1/2xx)y=color(red)(1/2xx)2log_2x`
`=>x=2^(y/2)`

`=>f^-1(x)=2^(x/2)`