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  4. There are relatively prime positive integers m and n so that ( m / n )= log 4(32 log 9 27), then the value of (m+n) is equal to

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Q. There are relatively prime positive integers $m$ and $n$ so that $\frac{ m }{ n }=\log _4\left(32^{\log _9 27}\right)$, then the value of $(m+n)$ is equal to

Continuity and Differentiability

Solution:

$\frac{ m }{ n }=\log _4\left(32^{\log _9 27}\right)=\log _4\left(32^{\frac{3}{2}}\right)=\log _4\left(2^{\frac{15}{2}}\right)=\frac{15}{4}$