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  4. Let a =((1/9))-2 log 3 7 and b =2- log (1/2)(7) then a =( b ) k where k is equal to

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Q. Let $a =\left(\frac{1}{9}\right)^{-2 \log _3 7}$ and $b =2^{-\log _{\frac{1}{2}}(7)}$ then $a =( b )^{ k }$ where $k$ is equal to

Continuity and Differentiability

Solution:

$a =9^{2 \log _3(7)}=9^{\log _3(49)}=3^{2 \log _3(49)}=3^{\log _3(2401)}=2401$
$b =2^{\log _2(7)=7} $
$\therefore a = b ^4 \Rightarrow k =4 A$