Question

Which of the following is the inverse of y=3*?3O y = log XOy -(o ;= logix

Answer 1

SOLUTION

We want to find the inverse of

$y=3^x$

First we will make x the subject. To do this, let us take log of both sides, we have

$\begin{gathered} log(y)=log(3^x) \\ log(3^x)=log(y)\text{ } \\ xlog3=log(y) \\ x=\frac{log(y)}{log3} \end{gathered}$

Now replace y with x, and x with y-inverse, we have

$\begin{gathered} x=\frac{log(y)}{log3} \\ y^{-1}=\frac{log(x)}{log3} \\ y^{-1}=log_3x \end{gathered}$

Hence the 2nd option is the correct answer