Question

Логарифмы. Вычислить

Answer 1

16)
$( \frac{1}{2} )^{6 log_{ \frac{1}{2} }(2) } = ( \frac{1}{2} )^{ log_{ \frac{1}{2} }( {2}^{6} ) } = {2}^{6} = 64$

17)
${7}^{ \frac{1}{2} log_{7}(9) } = {7}^{ log_{7}( {9}^{ \frac{1}{2} } ) } = {7}^{ log_{7}(3) } = 3$
18)
${9}^{ log_{3}(12 ) } = {3}^{2 log_{3}(12) } = {3}^{ log_{3}(12 ^{2} ) } = {12}^{2} = 144$
19)
${0.125}^{ log_{0.5}(1) } = {0.5}^{3 log_{0.5}(1) } = {0.5}^{ log_{0.5}( {1}^{3} ) } = {1}^{3} = 1$
20)
$( \frac{1}{9} )^{ \frac{1}{2} log_{3}(4) } = {3}^{ - 2 \times \frac{1}{2} log_{3}(4) } = {3}^{ - log_{3}(4) } = {3}^{ log_{3}( {4}^{ - 1} ) } = {4}^{ - 1} = \frac{1}{4}$
21)
${27}^{ - 4 log_{ \frac{1}{3} }(5) } = {( \frac{1}{3}) }^{ - 3 \times ( - 4) log_{ \frac{1}{3} }(5) } = {( \frac{1}{3} )}^{ 12log_{ \frac{1}{3} }(5) } = {( \frac{1}{3} )}^{ log_{ \frac{1}{3} }( {5}^{12} ) } = {5}^{12}$
22)
$( \frac{1}{7} )^{1 + 2 log_{ \frac{1}{7} }(3) } = {( \frac{1}{7}) }^{ log_{ \frac{1}{7} }( \frac{1}{7} ) + log_{ \frac{1}{7} }( 3^{2} ) } = ( \frac{1}{7} )^{ log_{ \frac{1}{7} }( \frac{1}{7} \times {3}^{2} ) } =( \frac{1}{7} )^{ log_{ \frac{1}{7} }( \frac{9}{7} ) } = \frac{9}{7}$
23)
$log_{10}(8) + log_{10}(125) = log_{10}(8 \times 125) = log_{10}(1000) = 3$

Answer 2

Решение на фото внизу