로그 관계식

$a ^{3} = b ^{2} = k \left( k \right.$는 $1$이 아닌 양수$\left. \right)$라 하면 $\displaystyle a = k ^{\frac{1}{3}}$, $\displaystyle b = k ^{\frac{1}{2}}$ $\displaystyle \log _{a} c = \log _{k ^{\frac{1}{3}}} c = 3 \log _{k} c$, $\displaystyle \log _{b} c = \log _{k ^{\frac{1}{2}}} c = 2 \log _{k} c$이므로 $\log _{a} c = \log _{b} c + 1$에서 $3 \log _{k} c = 2 \log _{k} c + 1$ $\log _{k} c = 1$, $c = k$ $\displaystyle \log _{c} ab = \log _{k} k ^{\frac{1}{3}} k ^{\frac{1}{2}} = \log _{k} k ^{\frac{5}{6}} = \frac{5}{6}$