If *f* (*x*) = \[\log_{x_2}\]write the value of *f*' (*x*).

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#### Solution

\[f(x) = \log_{x^2} x^3 \]

\[ = \frac{\log x^3}{\log x^2} (\text{ Change of base property })\]

\[ = \frac{3 \log x}{2 \log x}\]

\[ = \frac{3}{2}\]

\[f'\left( x \right) = 0 (\text{ Since } \frac{3}{2} \text{ is a constant })\]

Concept: The Concept of Derivative - Algebra of Derivative of Functions

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