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