Nếu ({log _8}3 = p), ({log _3}5 = q) thì log5 bằng

Câu hỏi:

Nếu \({\log _8}3 = p\), \({\log _3}5 = q\) thì log5 bằng

A.
\(\frac{{3pq}}{{1 + 3pq}}\)

B.
\({p^2} + {q^2}\)

C.
\(\frac{{3p + q}}{5}\)

D.
\(\frac{{1 + 3pq}}{p+q}\)

Đáp án đúng: A

\(\begin{array}{l}
\log 5 = \frac{{{{\log }_3}5}}{{{{\log }_3}10}} = \frac{{{{\log }_3}5}}{{{{\log }_3}2 + {{\log }_3}5}} = \frac{q}{{q + {{\log }_3}2}}\\
{\log _3}2 = \frac{{{{\log }_8}2}}{{{{\log }_8}3}} = \frac{{\frac{1}{3}{{\log }_2}2}}{{{{\log }_8}3}} = \frac{1}{{3p}}\\
\log 5 = \frac{q}{{q + \frac{1}{{3p}}}} = \frac{{3pq}}{{3pq + 1}}
\end{array}\)