Cho \({\log _2}5 = a;{\log _3}5 = b\). Tính \({\lo...

C

- Hướng dẫn giải

Ta có \({\log _2}3 = \frac{{{{\log }_5}3}}{{{{\log }_5}2}} = \frac{{{{\log }_2}5}}{{{{\log }_3}5}} = \frac{a}{b}\)

\(\begin{array}{l}
 \Rightarrow {\log _6}100 = \frac{{{{\log }_2}\left( {{2^3} \times {3^3} \times 5} \right)}}{{{{\log }_2}6}}\\
 = \frac{{3 + 3{{\log }_2}3 + {{\log }_2}5}}{{1 + {{\log }_2}5}}\\
 = \frac{{3 + \frac{{3a}}{b} + a}}{{1 + \frac{a}{b}}} = \frac{{3b + 3a + ab}}{{a + b}}
\end{array}\)