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  4. Find the value of ( log 5 9 ⋅ log 7 5 ⋅ log 3 7/ log 2 √6)+(1/ log 9 √6).

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Q. Find the value of $\frac{\log _5 9 \cdot \log _7 5 \cdot \log _3 7}{\log _2 \sqrt{6}}+\frac{1}{\log _9 \sqrt{6}}$.

Continuity and Differentiability

Solution:

$ \frac{\log _5 9 \cdot \log _7 5 \cdot \log _3 7}{\log _2 \sqrt{6}}+\frac{1}{\log _9 \sqrt{6}} $
$=\frac{\log _3 9}{\log _2 \sqrt{6}}+\frac{1}{\log _9 \sqrt{6}}=\frac{2}{\log _2 \sqrt{6}}+\frac{1}{\log _9 \sqrt{6}}=\frac{2}{\frac{1}{\log _{\sqrt{6}} 2}}+\frac{\frac{1}{\log _{\sqrt{6}} 9}}{}=2 \log _{\sqrt{6}} 2+\log _{\sqrt{6}} 9$
$=\log _{\sqrt{6}} 4+\log _{\sqrt{6}} 9=\log _{\sqrt{6}} 36=4$