로그의 이진 전개

$\displaystyle \log _{7} 2 = \frac{b _{1}}{2} + \frac{b _{2}}{2 ^{2}} + \frac{b _{3}}{2 ^{3}} + \frac{b _{4}}{2 ^{4}} + \cdots$ $\displaystyle 2 \log _{7} 2 = b _{1} + \frac{b _{2}}{2} + \frac{b _{3}}{2 ^{2}} + \frac{b _{4}}{2 ^{3}} + \cdots$ 또, $\displaystyle \log _{7} 4 = b _{1} + \frac{b _{2}}{2} + \frac{b _{3}}{2 ^{2}} + \frac{b _{4}}{2 ^{3}} + \cdots$ $\therefore b _{1} = 0$ $\displaystyle 2 \log _{7} 4 = b _{2} + \frac{b _{3}}{2} + \frac{b _{4}}{2 ^{2}} + \frac{b _{5}}{2 ^{3}} + \cdots$ $\displaystyle \log _{7} 16 = b _{2} + \frac{b _{3}}{2} + \frac{b _{4}}{2 ^{2}} + \frac{b _{5}}{2 ^{3}} + \cdots$ $\therefore b _{2} = 1$ $\displaystyle \log _{7} \frac{16}{7} = \frac{b _{3}}{2} + \frac{b _{4}}{2 ^{2}} + \frac{b _{5}}{2 ^{3}} + \cdots$ $\displaystyle 2 \log _{7} \frac{16}{7} = b _{3} + \frac{b _{4}}{2} + \frac{b _{5}}{2 ^{2}} + \cdots$ $\displaystyle \log _{7} ( \frac{16}{7} ) ^{2} = b _{3} + \frac{b _{4}}{2} + \frac{b _{5}}{2 ^{2}} + \cdots$ $\therefore b _{3} = 0$