로그함수 성질 보기

ㄱ. $\displaystyle \left\{ f \left( \frac{a}{5} \right) \right\} ^{2} = \left( \log _{5} \frac{a}{5} \right) ^{2} = ( \log _{5} a - 1 ) ^{2}$ $\displaystyle \left\{ f \left( \frac{5}{a} \right) \right\} ^{2} = \left( \log _{5} \frac{5}{a} \right) ^{2} = ( 1 - \log _{5} a ) ^{2}$ $\therefore$ 참 ㄴ. $f ( a + 1 ) - f ( a ) = \log _{5} ( a + 1 ) - \log _{5} a$$\displaystyle = \log _{5} \left( 1 + \frac{1}{a} \right)$ $f ( a + 2 ) - f ( a + 1 )$ $= \log _{5} ( a + 2 ) - \log _{5} ( a + 1 )$ $\displaystyle = \log _{5} \left( 1 + \frac{1}{a + 1} \right)$ $\displaystyle 1 + \frac{1}{a} > 1 + \frac{1}{a + 1}$이므로 $\displaystyle \log _{5} \left( 1 + \frac{1}{a} \right) > \log _{5} \left( 1 + \frac{1}{a + 1} \right)$ $\therefore$ 참 ㄷ. $f ^{- 1} ( x ) = 5 ^{x}$ $f ( a ) < f ( b )$이면 $a < b$ $a < b$이면 $f ^{-1} ( a ) < f ^{-1} ( b )$ $\therefore$ 참 따라서, ㄱ, ㄴ, ㄷ 모두 옳다.