Answer:
[tex]f^{-1}(x)=\frac{ln(x)}{ln(3)}[/tex]
Step-by-step explanation:
Given: [tex]f(x)=3^x[/tex]
To find the inverse, let's first replace the [tex]f(x)[/tex] with [tex]y[/tex].
[tex]y=3^x[/tex]
Switch the [tex]x[/tex] and [tex]y[/tex].
[tex]x=3^y[/tex]
Solve for [tex]y[/tex].
[tex]y=\frac{ln(x)}{ln(3)}[/tex]
Write it in inverse notation.
[tex]f^{-1}(x)=\frac{ln(x)}{ln(3)}[/tex]
