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1.Relation and Function
medium
The inverse of $y=5^{\log x}$ is
A
$x =5^{\text {logy }}$
B
$x=y^{\log 5}$
C
$x = y ^{\frac{1}{\log 5}}$
D
$x =5^{\frac{1}{\log y}}$
(JEE MAIN-2021)
Solution
Given $y=5^{\left(\log _{a} x\right)}=f(x)$
Interchanging $x \& y$ for inverse
$x=5^{\left(\log _{a} y\right)}=y^{\left(\log _{a} 5\right)}$
option $(1)$ or option $(2)$
Further, from given relation
$\log _{5} y =\log _{ a } x$
$\Rightarrow x=a^{\left(\log _{5} y\right)}=y^{\left(\log _{5} a\right)}$
$\Rightarrow x=y^{\left(\frac{1}{\log _{a} 5}\right)}=f^{-1}(y)$
Standard 12
Mathematics
