로그 관계식

$\displaystyle \log _{27} a = \log _{3 ^{3}} a = \frac{1}{3} \log _{3} a$, $\displaystyle \log _{3} \sqrt{b} = \log _{3} b ^{\frac{1}{2}} = \frac{1}{2} \log _{3} b$ 이므로 $\displaystyle \frac{1}{3} \log _{3} a = \frac{1}{2} \log _{3} b$ $\displaystyle \log _{b} a = \frac{\log _{3} a}{\log _{3} b} = \frac{3}{2}$ 따라서 $\displaystyle 20 \log _{b} \sqrt{a} = 10 \log _{b} a = 15$