For positive numbers \(A\), \(B\), and \(b\) but \(b \ne 1\),
$${\log _b}{A \over B} = {\log _b}A - {\log _b}B$$
Description: The logarithm of a quotient is the logarithm of the dividend (numerator) subtracted by the logarithm of the divisor (denominator).
Example 1:
$${\log _3}{x \over 2} = {\log _3}x - {\log _3}2$$
Example 2:
$${\log _7}{3 \over {10}} = {\log _7}3 - {\log _7}10$$
Example 3:
$$\eqalign{
{\log _6}7 &= {\log _6}{{14} \over 2} \cr
& = {\log _6}14 - {\log _6}2 \cr} $$