Question 693576
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \log_{\frac{1}{5}}\left(x^3\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \log_{\frac{1}{5}}\left(x^3\right)]


Solve for *[tex \LARGE y]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\log_{\frac{1}{5}}\left(x\right)\ =\ y]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_{\frac{1}{5}}\left(x\right)\ =\ \frac{y}{3}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \left(\frac{1}{5}\right)^{\frac{y}{3}}]


Swap variables


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \left(\frac{1}{5}\right)^{\frac{x}{3}}]


Replace *[tex \LARGE y] with *[tex \LARGE f^{-1}(x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f^{-1}(x)\ =\ \left(\frac{1}{5}\right)^{\frac{x}{3}}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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