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  4. If 3( log 3 5)x=5( log 5 3)2 then the value of x is equal to

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Q. If $3^{\left(\log _3 5\right)^x}=5^{\left(\log _5 3\right)^2}$ then the value of $x$ is equal to

Continuity and Differentiability

Solution:

$ \Theta 3^{\left(\log _3 5\right)^x}=\left(5^{\log _5 3}\right)^{\log _5 3} $
$=3^{\log _5 3} $
$\Rightarrow \left(\log _3 5\right)^x=\log _5 3=\frac{1}{\log _3 5}$
$x =-1$