Question

What is the correct inverse function for f(x)=In5x?

Answer 1

$y = \ln (5x)\\ e^y=5x\\ x=\dfrac{e^y}{5}\\ \boxed{f^{-1}(x)=\dfrac{e^x}{5}}$

Answer 2

$f(x)=\ln5x\\\\\ln5x=y\\\\e^{\ln5x}=e^y\iff5x=e^y\ \ \ |divide\ both\ sides\ by\ 5\\\\x=\dfrac{e^y}{5}\\\\\boxed{f^{-1}(x)=\dfrac{e^x}{5}}$