Differential co-efficient of $\log_{10}x$ w.r.t. $\log_{x} 10$ is
Answer & explanation
Correct answer: option 1
Let $y =\log_{10}x$ and $z=\log_x 10=\frac{1}{\log_{10}x}=\frac{1}{y}$
$∴y=\frac{1}{z}∴\frac{dy}{dz}=-\frac{1}{z^2}=-\frac{1}{(\log_x10)^2}=-\frac{(\log x)^2}{(\log 10)^2}$