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

1 Answer
Dec 18, 2015

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)