Cho \(a = {\log _3}2,b = {\log _5}2\). Khi đó \({\log _{16}}60\) bằng:

* Hướng dẫn giải

Ta có: \({\log _6}60 = \frac{{{{\log }_2}60}}{{{{\log }_2}16}} = \frac{{{{\log }_2}\left( {{2^2}.3.5} \right)}}{{{{\log }_2}{2^4}}} = \frac{1}{2}\left( {1 + \frac{1}{a} + \frac{1}{b}} \right) = \frac{1}{2}\left( {1 + \frac{{a + b}}{{ab}}} \right)\)