Question

................................ ​

Answer 1

Пошаговое объяснение:

$1) log_{2}(32) = log_{2}( {2}^{5} ) = 5$

$2) log_{32}(2) = log_{ {2}^{5} }(2) = \frac{1}{5} log_{2}(2) = 0.2$

$3) log_{8}(16) = log_{ {2}^{3} }( {2}^{4} ) = \frac{1}{3} \times 4 \times log_{2}(2) = \frac{4}{3}$

$4) {3}^{ log_{3}(7) } = 7$

$5) {4}^{2 log_{4}(5) } = {4}^{ log_{4}( {5}^{2} ) } = 25$

$6) {5}^{ log_{ {5}^{2} }(9) } = {5}^{ \frac{1}{2} log_{5}(9) } = {5}^{ log_{5}( {9}^{ \frac{1}{2} } ) } = 3$

$7) {5}^{ - log_{5}(3) } = {5}^{ log_{5}( {3}^{ - 1} ) } = \frac{1}{3}$

$8) {10}^{2 log_{10}(47) } = 47$

$9) {e}^{ - log_{e}(3) } = {e}^{ log_{e}( {3}^{ - 1} ) } = \frac{1}{3}$

$10) = lg(4 \times 25) = lg(100) = log_{10}(100) = 2$

$11) = log_{4}( \frac{100}{25} ) = log_{4}(4) = 1$

$12) log_{3}(21) - log_{3}(7) = log_{3}( \frac{21}{7} ) = log_{3}(3) = 1$

$13)1 + 0 + log_{5}( \frac{50}{2} ) = 1 + log_{5}(25) = 1 + 2 = 3$

$14) log_{3}( \frac{21}{7} ) + 0 = 1$

$16)0 + log_{5}( \frac{250}{2} ) = log_{5}(125) = 3$

$17)0 + lg( \frac{90}{9} ) = log_{10}(10) = 1$