Cho a=log3(2),b=log5(2) . Khi đó log16(60) bằng:

* Hướng dẫn giải

Ta có: 

$$\begin{gathered} {\log }_{16}\left(60\right)=\frac{{\log }_2\left(60\right)}{{\log }_2\left(16\right)}=\frac{{\log }_2\left(2^3.3.5\right)}{{\log }_2\left(2^4\right)} \\ =\frac{1}{2}\left(1+\frac{1}{a}+\frac{1}{b}\right)=\frac{1}{2}\left(1+\frac{a+b}{ab}\right) \end{gathered}$$

Đáp án D