Question

how the derivate of log x base 10 became log e base 10...just not understanding this single step...answer me immediately...there is my paper class 12th

Answer 1

Here the normal logarithm [just  $\log$ ]  is taken to the base 'e'.

To avoid confusion, let me indicate the base 'e' too there. Hence we get that line as,

$f(x)=\log_{10}x=\dfrac{\log_ex}{\log_e10}$

We take it as,

$\dfrac{\log_ex}{\log_e10}\ =\ \dfrac{1}{\log_e10}\cdot\log_ex\ =\ \dfrac{1}{\left(\dfrac{\log_m10}{\log_me}\right)}\cdot\log_ex\\\\\\=\ \dfrac{\log_me}{\log_m10}\cdot\log_ex\ =\ \log_{10}e\cdot\log_ex$

[m is some base.]

This is actually happened in the equation.

Also it is true that,

$\log_ba\ =\ \dfrac{1}{\log_ab}$