지수 연쇄 조건

$2 ^{a} = 3 ^{2}$, $3 ^{b} = 5 ^{3}$에서 $\displaystyle 3 = 2 ^{\frac{a}{2}}$, $\displaystyle 5 = 3 ^{\frac{b}{3}}$이므로 $\displaystyle 5 ^{c} = \left( 3 ^{\frac{b}{3}} \right) ^{c} = 3 ^{\frac{bc}{3}}$$\displaystyle = \left( 2 ^{\frac{a}{2}} \right) ^{\frac{bc}{3}} = 2 ^{\frac{abc}{6}}$ $\displaystyle = 2 ^{\frac{24}{6}} = 2 ^{4} = 16$