Cho log _ab = 2. Tính log _fracableft( a2b right).

Ta có
${\log _{\frac{a}{b}}}\left( {{a^2}b} \right) = 2{\log _{\frac{a}{b}}}a + {\log _{\frac{a}{b}}}b = \frac{2}{{{{\log }_a}\frac{a}{b}}} + \frac{1}{{{{\log }_b}\frac{a}{b}}} = \frac{2}{{1 - {{\log }_a}b}} + \frac{1}{{{{\log }_b}a - 1}} = \frac{2}{{1 - 2}} + \frac{1}{{\frac{1}{2} - 1}} = - 4.$