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  4. The differential coefficient of log 10 x with respect to is log x 10

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Q. The differential coefficient of $\log _{10} x$ with respect to is $\log _{x} 10$

Solution:

$\frac{\frac{d}{d x}\left(\frac{\log _{e}^{x}}{\log _{e}^{10}}\right)}{\frac{d}{d x}\left(\frac{\log _{e}^{10}}{\log _{e}^{x}}\right)}=-\left(\frac{\log _{e}^{x}}{\log _{e}^{10}}\right)^{2}=-\left(\log _{10}^{x}\right)^{2}$