How do you find the inverse of y=log_3 9x?

1 Answer
Jan 26, 2016

f^-1(x)=3^(x-2)

Explanation:

Given y=log_3(9x)

We know that if f(x)=y then f^-1(y)=x

So, from the above equation, by separating the log into 2 values, we get log_3(9x)=log_3(9)+log_3x
Since 9=3^2, the first term in the log value becomes log_3(9)=log_3(3^2)=2log_3(3)=2

So, y=2+log_3(x)\impliesy-2=log_3x

I believe you're familiar with this general log equation,
log_nm=p\impliesm=n^p

So, the above equation becomes 3^(y-2)=x
Taking for a fact that f^-1(y)=x#, we see what the inverse of the original function is.