상용로그 자연수 조건

$\displaystyle \frac{1}{4} < \log \sqrt{a} < \frac{11}{4}$, $\displaystyle \frac{7}{12} < \frac{1}{3} + \log \sqrt{a} < \frac{37}{12}$ $\displaystyle \frac{1}{3} + \log \sqrt{a} = 1$, $2$, $3$, $\displaystyle \log a = \frac{4}{3}$, $\displaystyle \frac{10}{3}$, $\displaystyle \frac{16}{3}$ $\displaystyle \log ( a _{1} \times a _{2} \times a _{3} ) = \frac{4}{3} + \frac{10}{3} + \frac{16}{3} = 10$ $\therefore$$a _{1} \times a _{2} \times a _{3} = 10 ^{10}$