Cho \({\log _2}5 = a,\,{\log _3}5 = b\). Khi đó \(...

B

- Hướng dẫn giải

Ta có: \({\log _2}5 = a,\,{\log _3}5 = b\)

\(\Rightarrow \left\{ \begin{array}{l}{\log _5}2 = \dfrac{1}{a}\\{\log _5}3 = \dfrac{1}{b}\end{array} \right.\)

Khi đó ta có: \({\log _5}6 = {\log _5}2 + {\log _5}3 = \dfrac{1}{a} + \dfrac{1}{b} = \dfrac{{a + b}}{{ab}} \)

\(\Rightarrow {\log _6}5 = \dfrac{{ab}}{{a + b}}\)