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Question
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Solution
\[f(x) = \log_{x^2} x^3 \]
\[ = \frac{\log x^3}{\log x^2} (\text{ Change of base property })\]
\[ = \frac{3 \log x}{2 \log x}\]
\[ = \frac{3}{2}\]
\[f'\left( x \right) = 0 (\text{ Since } \frac{3}{2} \text{ is a constant })\]
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