Nếu {log _8}3 = p) và ({log _3}5 = q thì log 5 bằng:

$\begin{array}{l} \log 5 = \frac{1}{{{{\log }_5}10}} = \frac{1}{{{{\log }_5}2 + {{\log }_5}5}} = \frac{1}{{{{\log }_5}2 + 1}} = \frac{1}{{\frac{1}{{{{\log }_2}3.{{\log }_3}5}} + 1}}\\  = \frac{1}{{\frac{1}{{3{{\log }_3}5.{{\log }_8}3}} + 1}} = \frac{1}{{\frac{1}{{3pq}} + 1}} = \frac{{3pq}}{{1 + 3pq}}. \end{array}$