SOLUTION
We want to find the inverse of
[tex]y=3^x[/tex]
First we will make x the subject. To do this, let us take log of both sides, we have
[tex]\begin{gathered} log(y)=log(3^x) \\ log(3^x)=log(y)\text{ } \\ xlog3=log(y) \\ x=\frac{log(y)}{log3} \end{gathered}[/tex]
Now replace y with x, and x with y-inverse, we have
[tex]\begin{gathered} x=\frac{log(y)}{log3} \\ y^{-1}=\frac{log(x)}{log3} \\ y^{-1}=log_3x \end{gathered}[/tex]
Hence the 2nd option is the correct answer
