a) Ta có \(1350 = 30.3^2 .5\) suy ra
\(lo{g_{30}}1350 =lo{g_{30}}(30.{3^2}.5) \\= log_{30}30 + log_{30}3^2+log_{30}5\\ =1 + 2lo{g_{30}}3 + lo{g_{30}}5 = 1 + 2a+b.\)
b) Ta có: \(lo{g_{25}}15 = \dfrac{1}{log_{15}25}=\dfrac{1}{log_{15}5^2} \\= \dfrac{1}{2log_{15}5}= \dfrac{1}{2log_{15}\left ( 15: 3 \right )} \) \(= \dfrac{1}{2\left (log_{15}15-log_{15}3 \right )} \\ = \dfrac{1}{2\left (1-log_{15}3 \right )} = \dfrac{1}{2\left (1-c \right )}\)
