Question

математика задание 1 3 4 5 6

Answer 1

Ответ:

1.

$\frac{ {a}^{3} \times ( {a}^{ - 3}) ^{ - \frac{2}{3} } }{ {a}^{4} } = \\ = \frac{ {a}^{3} \times {a}^{ - 3 \times (- \frac{2}{3}) } }{ {a}^{4} } = {a}^{3 + 2 - 4} = a$

3.

${3}^{1 - x} < \frac{1}{81} \\ {3}^{1 - x} < {3}^{ - 4} \\ 1 - x < - 4 \\ x > 5$

4.

$log_{5}24 - log_{5}120 - log_{5}5 = \\ = log_{5}( \frac{24}{120} ) - 1 = log_{5} \frac{1}{5} - 1 = \\ = log_{5}5 ^{ - 1} - 1 = - 1 - 1 = - 2$

5.

$( { log_{3}x})^{2} - 6 log_{3}x + 9 = 0$

замена:

$log_{3}x = t$

$t^{2} - 6t + 9 = 0 \\ (t - 3)^{2} = 0 \\ t = 3$

возвращаемся к замене

$log_{3}x = 3 \\ x = {3}^{3} = 27$

6.

$log_{10}0.5x < - 2$

ОДЗ:

0,5х>0

х>0

$0.5x < {10}^{ - 2} \\ 0.5x < \frac{1}{100} \\ x < \frac{1}{50}$

$x∈(0; \frac{1}{50} )$