Question

How do I find the inverse of y=log⬇1/4 x^5

Answer 1

`f(x)=\log_{\tfrac{1}{4}}x^5\\ y=\log_{\tfrac{1}{4}}x^5\\ \left((1)/(4)\right)^y=x^5\\ x=\left(\left((1)/(4)\right)^y\right)^{(1)/(5)}\\ x=\left((1)/(4)\right)^{(y)/(5)}\\x=\left(2^(-2)\right)^{(y)/(5)}\\x=2^{-\tfrac{2y}{5}}\\ f^(-1)(x)=2^{-\tfrac{2x}{5}}`