Question

Помогите пожалуйста, весь 3 вариант

Answer 1

Ответ:

$1)8 \times {8}^{ log_{8}(6) } = 8 \times 6 = 48$

$2) {9}^{ log_{3}(2) } = {3}^{2 log_{3}(2) } = {3}^{ log_{3}(4) } = 4$

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

$4)1$

$5) log_{6}( {6}^{3} ) \times log_{9}( {9}^{4} ) = 3 \times 4 \times log_{6}(6) \times log_{9}(9) = 12$

$6) log_{6}( \frac{54}{1.5} ) = log_{6}(36) = 2$

$7) log_{8}( \frac{80}{1.25} ) = log_{8}(64) = 2$

$8)1 + log_{ {5}^{ - 1} }( {5}^{4} ) = 1 - 1 \times 4 \times log_{5}(5) = 1 - 4 = - 3$

$9) log_{0.55}( \frac{20}{11} ) = log_{ \frac{55}{100} }( \frac{20}{11} ) = log_{ \frac{11}{20} }(( { \frac{11}{20} )}^{ - 1} ) = - 1$

$10) log_{5}(20) + log_{5}(0.05) = log_{5}(20 \times 0.05) = log_{5}(1) = 0$

$11) log_{ \frac{2}{5} }(9) \times log_{9}( \frac{5}{2} ) = log_{ \frac{2}{5} }(9) \times log_{9}( ({ \frac{2}{5}) }^{ - 1} ) = - 1$

$12) log_{3}(13) \times log_{13}( {3}^{2} ) = 2$

$13)(1 - log_{ {2}^{2} }( {2}^{5} ) )(1 - log_{2}( {2}^{5} ) ) = (1 - \frac{1}{2} \times 5)(1 - 5) = - \frac{3}{2} \times ( - 4) = 6$

$17) \frac{ log_{4}(80) }{ log_{4}(16) + log_{4}(5) } = \frac{ log_{4}(80) }{ log_{4}(16 \times 5) } = \frac{ log_{4}(80) }{ log_{4}(80) } = 1$

$18) \frac{ log_{6}( {2}^{2} ) }{ log_{6}(2) } = \frac{2 log_{6}(2) }{ log_{6}(2) } = 2$

$19) \frac{ log_{7}(2) }{ log_{ {7}^{ \frac{1}{2} } }(2) } = \frac{ log_{7}(2) }{2 log_{7}(2) } = \frac{1}{2} = 0.5$

$20) {2}^{ log_{ {2}^{2} }(16) } = {2}^{ \frac{1}{2} log_{2}(16) } = {2}^{ log_{2}(4) } = 4$

$21) { log_{ {15}^{ \frac{1}{2} } }(3375) }^{2} = { \frac{1}{2} }^{2} \times log_{15}(3375) = \frac{1}{4} \times 3 = 0.75$

$22) {9}^{ log_{9}( {8}^{2} ) } = 64$

$23) {5}^{2 log_{5}( \sqrt{8} ) } = {5}^{ log_{5}( { \sqrt{8} }^{2} ) } = 8$

$24) log_{16}(4) = \frac{1}{2} = 0.5$

$25) \frac{30}{ {3}^{ log_{3}(2) } } = \frac{30}{2} = 15$

$26) log_{ \frac{2}{5} }( \sqrt{ \frac{5}{2} } ) = log_{ \frac{2}{5} }( { \frac{2}{5} }^{ - \frac{1}{2} } ) = - \frac{1}{2} = - 0.5$