Question

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

Answer 1

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

Answer 2

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