Логарифм 9 по основанию 3 - логарифм 27 по основанию 9

1-ый способ: [latex] \log_3{9} = 2 [/latex] , поскольку [latex] 3^2=9 [/latex] ; [latex] \log_9{27} = 1.5 [/latex] , поскольку [latex] 9^{1.5}= 9^{ \frac{3}{2} } = ( \sqrt{9} )^3 = 27 [/latex] ; [latex] \log_3{9} - \log_9{27} = 2 - 1.5 = 0.5 = \frac{1}{2} [/latex] ; 2-ой способ: [latex] \log_3{9} - \log_9{27} = \frac{ \log_3{9} }{ \log_3{3} } - \frac{ \log_3{27} }{ \log_3{9} } = 2 - \frac{3}{2} = 2 - 1.5 = 0.5 = \frac{1}{2} [/latex] ; 3-ий способ: [latex] \log_3{9} - \log_9{27} = \log_{3^2}{9^2} - \log_9{27} = \log_9{9^2} - \log_9{27} = [/latex] [latex] = \log_9{ \frac{81}{27} } = \log_9{3} = \frac{1}{ \log_3{9} } = \frac{1}{2} = 0.5 [/latex] ;