The inverse of [y = 5^ x] is : · questionr

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Joint Entrance Examination
Mathematics
Functions
Question 67

Question 67 of 162EasyMCQ

The inverse of \[y = {5^{\log x}}\] is :

A

x={5}^{\log y}

B

x={y}^{\frac{1}{\log 5}}

C

x={5}^{\frac{1}{\log y}}

D

x={y}^{\log 5}

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Solutions · 1

Official solution

\[y = {5^{\log x}}\] \[ \Rightarrow \log y = \log x.log5\] \[ \Rightarrow \log x = {{\log y} \over {\log 5}} = {\log _5}y\] \[ \Rightarrow x = {e^{{{\log }_5}y}}\] \[ \Rightarrow x = {y^{{{\log }_5}e}}\] \[ \Rightarrow x = {y^{{1 \over {\log 5}}}}\]

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