Đề bài

Cho \({\log _a}b = 2\). Tính: a)    \({\log _a}\left( {{a^2}b^3} \right)\) b)    \({\log _a}\frac{{a\sqrt a }}{{b\sqrt[3]{b}}}\) c)     \({\log _a}(2b) + {\log _a}\left( {\frac{{{b^2}}}{2}} \right)\)

Lời giải chi tiết

a)    \({\log _a}\left( {{a^2}b^3} \right) = {\log _a}{a^2} + {\log _a}b^3 = {\log _a}{a^2} + 3{\log _a}b= 2 + 3.2 = 8\)b)    \({\log _a}\frac{{a\sqrt a }}{{b\sqrt[3]{b}}} = {\log _a}a.{a^{\frac{1}{2}}} - {\log _a}b.{b^{\frac{1}{3}}} = {\log _a}{a^{\frac{3}{2}}} - {\log _a}{b^{\frac{4}{3}}} = \frac{3}{2} - \frac{4}{3}.2 = \frac{3}{2} - \frac{8}{3} =  - \frac{7}{6}\)c)     \({\log _a}(2b) + {\log _a}\left( {\frac{{{b^2}}}{2}} \right) = {\log _a}\left( {\frac{{2b.{b^2}}}{2}} \right) = {\log _a}{b^3} = 3.2 = 6\)