Question

вычислите: a)log9(log3 125)
б) log2 25÷ log2 5​

Answer 1

Ответ:

а) $\boxed{\log_{9}{(\log_{3}{125})} =0,5 + \log_{9}{(\log_{3}{5})} }$

б) $\boxed{ \dfrac{\log_{2}{25} }{\log_{2}{5}} = 2}$

Объяснение:

а) $\log_{9}{(\log_{3}{125})} = \log_{9}{(\log_{3}{5^{3}})} = \log_{9}{(3\log_{3}{5})} = \log_{9}{3} + \log_{9}{(\log_{3}{5})} =$

$= \log_{3^{2}}{3} + \log_{9}{(\log_{3}{5})} =\dfrac{1}{2}\cdot \log_{3}{3} + \log_{9}{(\log_{3}{5})} = 0,5 + \log_{9}{(\log_{3}{5})}$

б) $\dfrac{\log_{2}{25} }{\log_{2}{5}} = \log_{5}{25} = \log_{5}{5^{2}} = 2 \log_{5}{5} = 2 \cdot 1 = 2$