3 years ago

What is the correct inverse function for f(x)=In5x?

Mathematics

2 answers:

telo118 [61]3 years ago

8 0

$y = \ln (5x)\\
e^y=5x\\
x=\dfrac{e^y}{5}\\
\boxed{f^{-1}(x)=\dfrac{e^x}{5}}$

Mashutka [201]3 years ago

8 0

$f(x)=\ln5x\\\\\ln5x=y\\\\e^{\ln5x}=e^y\iff5x=e^y\ \ \ |divide\ both\ sides\ by\ 5\\\\x=\dfrac{e^y}{5}\\\\\boxed{f^{-1}(x)=\dfrac{e^x}{5}}$

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