Question

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

Answer 1

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=(log(y))/(log3) \end{gathered}`

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

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

Hence the 2nd option is the correct answer