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  4. The value of 'a' for which ( log a 7/ log 6 7)= log π 36 holds good, is

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Q. The value of 'a' for which $\frac{\log _a 7}{\log _6 7}=\log _\pi 36$ holds good, is

Continuity and Differentiability

Solution:

$ \log _{ a } 7 \cdot \log _7 6=\log _\pi 36$
$\log _a 6=2 \log _\pi 6=\frac{\log _\pi 6}{\log _\pi a}=2 \log _\pi 6 \Rightarrow \log _\pi a=\frac{1}{2} \Rightarrow a=\sqrt{\pi}$