Biết \({\log _{40}}75 = a + \frac{{{{\log }_2}3 -...

B

- Hướng dẫn giải

\(\begin{array}{l}
{\log _{40}}75 = \frac{{{{\log }_2}75}}{{{{\log }_2}40}} = \frac{{{{\log }_2}3 + 2{{\log }_2}5}}{{{{\log }_2}40}}\\
 = \frac{{{{\log }_2}3 + 2\left( {{{\log }_2}40 - 3} \right)}}{{{{\log }_2}40}} = 2 + \frac{{{{\log }_2}3 - 6}}{{3 + {{\log }_2}5}}
\end{array}\)

Suy ra \(a = 2,\,b = 6,\,c = 3\)

Vậy \(abc = 2.6.3 = 36\).