Logarithmic function basics for JEE

Formula

\[y=\log_a x=\frac{\ln x}{\ln a}\ (a>0,a\neq 1),\qquad \ln x=\log_e x\]

Variables: \(a\) is base, \(x>0\).

Conditions: Logarithm defined only for positive argument.

Change of base, derivatives, continuity and inverse function questions.