Biết \({\log _{40}}75 = a +...

B

- Hướng dẫn giải

\({\log _{40}}75 = \dfrac{{{{\log }_2}75}}{{{{\log }_2}40}} \\= \dfrac{{{{\log }_2}3 + 2{{\log }_2}5}}{{{{\log }_2}40}} \\= \dfrac{{{{\log }_2}3 + 2\left( {{{\log }_2}40 - 3} \right)}}{{{{\log }_2}40}} \\= 2 + \dfrac{{{{\log }_2}3 - 6}}{{3 + {{\log }_2}5}}\)

Suy ra a = 2, b = 6, c = 3.

Vậy abc = 2.6.3 = 36