로그 가수 방정식

$N$은 두 자리의 자연수이므로 $\log N = 1 + \alpha$ $\displaystyle \frac{1}{2} + 1 + \alpha = \alpha + \frac{1}{2} \left( \frac{1 + \alpha}{\log 2} - 3 \right)$, $\displaystyle \frac{3}{2} = \frac{1}{2} \left( \frac{1 + \alpha}{\log 2} - 3 \right)$ $\displaystyle 3 = \frac{1 + \alpha}{\log 2} - 3$, $\displaystyle 6 = \frac{1 + \alpha}{\log 2}$ $\log N = 1 + \alpha = 6 \log 2 = \log 64$ $\therefore N = 64$