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Mkilts17
Mkilts17 Mkilts17
  • 26-07-2016
  • Mathematics
Answered

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

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konrad509
konrad509 konrad509
  • 26-07-2016

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



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dalendrk
dalendrk dalendrk
  • 26-07-2016

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

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