Cho log 2(3) = a. Tính T = log 36(24) theo a

* Hướng dẫn giải

Đáp án D

Ta có: $$\begin{gathered} T={\log }_{36}24=\frac{1}{2}{\log }_6\left(6.4\right)=\frac{1}{2}\left(1={\log }_{6}4\right) \\ =\frac{1}{2}\left(1+\frac{2}{{\log }_{2}6}\right)=\frac{1}{2}\left(1+\frac{2}{1+{\log }_{2}3}\right) \end{gathered}$$

$=\frac{1}{2}\left(1+\frac{2}{1+a}\right)=\frac{a+3}{2a+2}$