Question

help!! (помогите) пишу так много потому что znanija требуют 20 символов, примеры в скриншоте.

Answer 1

Ответ:

1.

$log_{12}( \frac{7}{144} ) - log_{12}(7) = log_{12}(7) - log_{12}(144) - log_{12}(7) = - 2$

2.

$log_{4}(400) + log_{4}(0.16) = log_{4}(400 \times 0.16) = \\ = log_{4}(4 \times 16) = 3$

3.

$log_{9}(81) - log_{3}(27) + log_{ \frac{1}{3} }(3) = \\ = 2 - 3 - 1 = - 2$

4.

$5 log_{3}(81) = 5 \times 4 = 20$

5.

$12 - {10}^{lg5} = 12 - {10}^{ log_{10}(5) } = 12 - 5 = 7$

6.

${32}^{ log_{0.5}( \sqrt[5]{7} ) } = {2}^{5 log_{ {2}^{ - 1} }( {7}^{ \frac{1}{5} } ) } = {2}^{5 \times ( - 1) \times \frac{1}{5} log_{2}(7) } = \\ = {2}^{ - log_{2}(7) } = {2}^{ log_{2}( {7}^{ - 1} ) } = \frac{1}{7}$

7.

$4 log_{4}(2) \times log_{2}(4) + 2 = 4 \times \frac{1}{2} \times 2 + 2 = \\ = 4 + 2 = 6$

8.

$lg( \frac{100}{ {b}^{3} } ) = lg(100) - lg {b}^{3} = 2 - 3lgb = \\ = 2 - 3 \times 3 = 2 - 9 = - 7$

9.

$log_{3}( {a}^{ \frac{3}{7} } ) = \frac{3}{7} log_{3}(a) = \frac{3}{7} \times 21 = 9$

10.

$lg(100a) = lg100 + lga = 2 + lga = \\ \\ lga {}^{2} = 2 lga \\ 2lga = 6 \\ lga = 3 \\ \\ = 2 + 3 = 5$