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  4. Let a = log 3 and b =( log 3/ log ( log 3))( All logarithms on base 10). The number a b is

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Q. Let $a =\log 3$ and $b =\frac{\log 3}{\log (\log 3)}($ All logarithms on base 10$)$. The number $a ^{ b }$ is

Continuity and Differentiability

Solution:

Let $\log _{10} 3= x$
$\therefore b=\frac{x}{\log x} \text { and } a=x $
$\Rightarrow a^b=x^{\frac{x}{\log x}}=x^{x \log _x 10}=x^{\log _x 10^x}=10^x=10^{\log _{10} 3}=3 $