Exponential function basics for JEE

Formula

\[a^x=e^{x\log a}\ (a>0,a\neq 1),\qquad e^x>0\ \forall x\]

Variables: \(a\) is positive base, \(e\) is Euler's number.

Conditions: Real-valued exponential requires \(a>0\).

Transforming exponentials, limits, differentiation, monotonicity.