Question

Прикрепите решение в виде файла/рисунка

Answer 1

Ответ:

а)

$log_{0.6}( log_{8}(32) ) + 49 {}^{ log_{ \sqrt{7} }( \sqrt{2} ) } = \\ = log_{0.6}( log_{ {2}^{3} }( {2}^{5} ) ) + {49}^{ log_{ {7}^{ \frac{1}{2} } }( \sqrt{2} ) } = \\ = log_{0.6}( \frac{5}{3} log_{2}(2) ) + {7}^{2 \times 2 log_{7}( \sqrt{2} ) } = \\ = log_{ \frac{3}{5} }( \frac{5}{3} ) + {7}^{ log_{7}( {( \sqrt{2}) }^{4} ) } = \\ = - 1 + 4 = 3$

б)

$\frac{lg900 - 2}{2lg0.5 + lg12} = \frac{lg900 - lg100}{lg {(0.5)}^{2} + lg12} = \\ = \frac{lg \frac{900}{100} }{lg (\frac{1}{4} \times 12) } = \frac{lg9}{lg3} = log_{3}(9) = 2$