Cho \(c = {\log _{15}}3.\)

C

- Hướng dẫn giải

Ta có: \(c = {\log _{15}}3\)

\(\Leftrightarrow \dfrac{1}{c} = {\log _3}15 = {\log _3}\left( {3.5} \right) = {\log _3}5 + 1\)

\(\Rightarrow {\log _3}5 = \dfrac{1}{c} - 1 = \dfrac{{1 - c}}{c}\)

\(\Leftrightarrow {\log _5}3 = \dfrac{c}{{1 - c}}\)

Khi đó ta có:

\({\log _{25}}15 = \dfrac{1}{2}{\log _5}\left( {3.5} \right)\)

\(= \dfrac{1}{2}\left( {1 + {{\log }_5}3} \right)\)

\(= \dfrac{1}{2}\left( {1 + \dfrac{c}{{1 - c}}} \right)\)

\(= \dfrac{1}{{2\left( {1 - c} \right)}}\)