Đáp án:
Chọn D.
Giải thích các bước giải:
$\begin{array}{l}
{\log _5}3 = a;\,\,\,{\log _2}5 = b\\
\Rightarrow {\log _2}3 = {\log _2}5.{\log _5}3 = ab\\
\Rightarrow {\log _3}2 = \frac{1}{{ab}}.\\
{\log _{24}}15 = {\log _{24}}3 + {\log _{24}}5 = \frac{1}{{{{\log }_3}24}} + \frac{1}{{{{\log }_5}24}}\\
= \frac{1}{{{{\log }_3}3 + {{\log }_3}8}} + \frac{1}{{{{\log }_5}3 + {{\log }_5}8}}\\
= \frac{1}{{1 + 3{{\log }_3}2}} + \frac{1}{{{{\log }_5}3 + 3{{\log }_5}2}}\\
= \frac{1}{{1 + 3.\frac{1}{{ab}}}} + \frac{1}{{a + \frac{3}{b}}} = \frac{{ab}}{{ab + 3}} + \frac{b}{{ab + 3}} = \frac{{ab + b}}{{ab + 3}}.
\end{array}$
