Question

Help with inverse logs

Answer 1

find f^-1
\[f(x)=2^{x}\]

Answer 2

well, just like any other inverses, you just switch about the letters

\(\bf f(x) = 2^x\implies y = 2^x\\ \quad \\
f^{-1}(x) \implies x = 2^y\\ \quad \\
\textit{log cancellation rule of }\quad log_aa^x = x\\ \quad \\
x = 2^y\implies log_2(x) = log_2(2^y)\implies log_2(x) = y\)