Question

помагите решить пожалуйста:(​

Answer 1

Ответ:

$log_{125}5 = log_{ {5}^{3} }5 = \frac{1}{3}log_{5}5 = \frac{1}{3} \\ log_{ \sqrt{7} } \sqrt{49} = log_{ \sqrt{7} }7 = log_{ {7}^{ \frac{1}{2} } }7 = \frac{1}{ \frac{1}{2} } log_{7}7 = 2 \\ log_{ \sqrt{7} }49 = log_{ {7}^{ \frac{1}{2} } } {7}^{2} = \frac{2}{ \frac{1}{2} } log_{7}7 = 4 \\ log_{ \sqrt{5} } \sqrt {625} = log_{ {5}^{ \frac{1}{2} } }25 = 2 log_{5} {5}^{2} = 2 \times 2 log_{5}5 = 4 \\ log_{2}0.125 + log_{ \sqrt{3} }9 = log_{2} {2}^{ - 3} + log_{ {3}^{ \frac{1}{2} } } {3}^{2} = - 3 + \frac{2}{ \frac{1}{2} } = - 3 + 4 = 1$

$log_{2} log_{2} \sqrt{ \sqrt[4]{2} } = log_{2} log_{2} {2}^{ \frac{1}{8} } = \\ = log_{2} \frac{1}{8} log_{2}2 = log_{2} \frac{1}{8 } = \\ = log_{2} {2}^{ - 3} = - 3 log_{2}2 = - 3$