Question

If f (x) = ${\log }_{x_2}$ x³, write the value of f' (x).

Answer 1

$$\begin{gathered} f\left(x\right)={\log }_{x^2}{x}^3 \\ =\frac{\log x^3}{\log x^2}(\mathrm{Change}\mathrm{of}\mathrm{base}\mathrm{property}) \\ =\frac{3\log x}{2\log x} \\ =\frac{3}{2} \\ f\text{'}\left(x\right)=0(\mathrm{Since}\frac{3}{2}\mathrm{is}\mathrm{a}\mathrm{constant}) \end{gathered}$$