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  4. log 3(( log 3 3333/ log 33 333)) has the value equal to

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Q. $\log _3\left(\frac{\log _3 3^{3^{3^3}}}{\log _{3^3} 3^{3^3}}\right)$ has the value equal to

Continuity and Differentiability

Solution:

$\log _3\left(\frac{3^{3^3}}{3^2}\right) \quad=\log _3\left(\frac{3^{27}}{3^2}\right) \quad\left[\log _{3^3} 3^{3^3}=\frac{\log _3 3^{3^3}}{\log _3 3^3}=\frac{3^3}{3}=3^2\right]$
$=\log _3\left(3^{25}\right)=25$