Logarithm laws for JEE

Formula

\[\log_a(xy)=\log_a x+\log_a y,\quad \log_a\!\left(\frac{x}{y}\right)=\log_a x-\log_a y,\quad \log_a(x^r)=r\log_a x\]

Variables: \(a>0,a\neq 1\), \(x,y>0\), \(r\in\mathbb R\).

Conditions: Arguments must be positive in real domain.

Log differentiation, simplification before limits and derivatives.