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ㄱ. $1 < a < b$에서 $0 < \log a < \log b$이다. $\displaystyle \log _{b} a = \frac{\log a}{\log b} < \frac{\log b}{\log a} = \log _{a} b$(참) ㄴ. (반례) $a = 10 , b = 100$일 때 $10 < 100$이지만 $\displaystyle \frac{1}{10} \mathrm{\log} 10 > \frac{1}{100} \mathrm{\log} 100$(거짓) ㄷ. $2 \log ( a + b ) < \log 2 ( a ^{2} + b ^{2} ) \leftrightarrow \log ( a + b ) ^{2} < \log 2 ( a ^{2} + b ^{2} )$ $2 ( a ^{2} + b ^{2} ) - ( a + b ) ^{2} = a ^{2} - 2 ab + b ^{2} = ( a - b ) ^{2} > 0 ( \because a < b )$ $( a + b ) ^{2} < 2 ( a ^{2} + b ^{2} )$ $\therefore 2 \log ( a + b ) < \log 2 ( a ^{2} + b ^{2} )$(참)