Question

Inverse of f(x) = 3^x

Answer 1

Consider:
\[f(x)=y=3^x\]
Replace the y with x and the x with y (since you are reflecting it about the line y=x. Giving:
\[g(y)=x=3^y\]
Take the log base 3 of both sides giving:
\[\log_3(x)=\log_3(3^y)=y\]
Using the identity:
\[\log_a(a^b)=b\]