Quotient Law of Logarithms

Quotient Law

${\log }_b(\frac{m}{n})={\log }_b(m)-{\log }_b(n)$

Proof

$x={\log }_{b}m$ $b^x=m$ $y={\log }_b(n)$ $b^y=n$ divide them $\frac{b^x}{b^y}=\frac{m}{n}$ $b^{x-y}=\frac{m}{n}$ $x-y=\log (\frac{m}{n})$ ${\log }_{b}m-{\log }_{b}n={\log }_b(\frac{m}{n})$