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Question
logx2 x
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Solution
\[\log_{x^2} x = \frac{\log x}{\log x^2} (\text{ by change of base property })\]
\[ = \frac{\log x}{2 \log x} \left[ \log x^2 = 2 \log x \right]\]
\[ = \frac{1}{2}\]
\[\text{ Now }\frac{d}{dx}\left( \log_{x^2} x \right)=\frac{d}{dx}\left( \frac{1}{2} \right)\]
\[ = 0 \left( \because\frac{1}{2}\text{ is a constant } \right )\]
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