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  4. If log a b=2, log b c=3 and log 4 c= log 4 a+5, then (a+b) is equal to

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Q. If $\log _a b=2, \log _b c=3$ and $\log _4 c=\log _4 a+5$, then $(a+b)$ is equal to

Continuity and Differentiability

Solution:

$ b=a^2 \text { and } c=b^3=a^6 $
$\therefore \log _4 a^6=\log _4 a+5 \Rightarrow 5 \log _4 a=5 \Rightarrow a=4$
$\therefore b=16 $
$\therefore a+b=20$