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  4. If 2 log 3 P =5, then p log 5 4 equals

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Q. If $2^{\log _3 P }=5$, then $p ^{\log _5 4}$ equals

Continuity and Differentiability

Solution:

$2^{\log _3 P }=5 \Rightarrow \log _3 p \log _5 2=1 \Rightarrow \log _3 p =\log _2 5$
$\Rightarrow p =3^{\log _2 5}$
$\Rightarrow( p )^{\log _5 4}=\left(3^{\log _2 5}\right)^{\log _5 4}=3^{\log _2 5 \cdot 2 \log _5 2}=3^2=9$