Cho \(a = {\log _7}5,b = {\log _3}5.\) Biểu thức \(M = {\log _{21}}5\) bằng

* Hướng dẫn giải

\(\begin{array}{l}{\log _{21}}5 = \dfrac{1}{{{{\log }_5}21}} = \dfrac{1}{{{{\log }_5}3 + {{\log }_5}7}} = \dfrac{1}{{\dfrac{1}{{{{\log }_3}5}} + \dfrac{1}{{{{\log }_7}5}}}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{1}{{\dfrac{1}{a} + \dfrac{1}{b}}} = \dfrac{1}{{\dfrac{{a + b}}{{ab}}}} = \dfrac{{ab}}{{a + b}}.\end{array}\) 

Chọn  B.