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balandron [24]
3 years ago
5

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

Mathematics
1 answer:
Reil [10]3 years ago
5 0
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}}


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