Question

Ребят, кто шарит помогите пожалуйста! 50баллов
С решением пожалуйста

Answer 1

$log_{0.3}( frac{1}{0.09} ) = - 2$

$log_{2}( log_{2}( sqrt[4]{2} ) ) = log_{2}( log_{2}( {2}^{ frac{1}{4} } ) ) = log_{2}( frac{1}{4} ) = - 2$

$log_{6}(8) - log_{6}(2) + log_{6}(9) = log_{6}( frac{8 times 9}{2} ) = log_{6}(36) = 2$

$log_{2}( log_{2}( sqrt[4]{2} ) ) = log_{2}( log_{2}( {2}^{ frac{1}{4} } ) ) = log_{2}( frac{1}{4} ) = - 2 \ log_{5}(8) - log_{5}(2) + log_{5}( frac{25}{4} ) = log_{5}( frac{8 times 25}{2 times 4} ) = log_{5}(25) = 2$

$log_{35}(7) + frac{1}{ log_{5}(35) } = log_{35}(7) + log_{35}(5) = log_{35}(7 times 5) = log_{35}(35) = 1$

$log_{ sqrt{7} }( frac{1}{7} ) + {3}^{ log_{3}(7) } = log_{ sqrt{7} }( frac{1}{7} ) + 7 = - 2 + 7 = 5$

${ sqrt{5} }^{ log_{5}(16) } = { ({5}^{ frac{1}{2} }) }^{ log_{5}(16) } = { ({5}^{ log_{5}(16) } )}^{ frac{1}{2} } = {16}^{ frac{1}{2} } = 4$

${10}^{1 - log(5) } = {10}^{1} div {10}^{ log(5) } = 10 div 5 = 2$

$( log_{5}(36) + log_{5}(2) - log_{5}(8) ) log_{9}( frac{1}{25} ) = log_{5}( frac{36 times 2}{8} ) log_{9}( frac{1}{25} ) = log_{5}(9) log_{9}( frac{1}{25} ) = log_{5}(9) log_{9}( {( 5)}^{ - 2} ) = - 2 log_{5}(9) log_{9}(5) = frac{ - 2 log_{5}(9) }{ log_{5}(9) } = - 2$

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

$log_{2}( frac{2}{3} ) + log_{4}( frac{9}{4} ) = log_{2}( frac{2}{3} ) + log_{ {2}^{2} }( { frac{3}{2} )}^{2} ) = log_{2}( frac{2}{3} ) + log_{2}( frac{3}{2} ) = log_{2}( frac{2}{3} times frac{3}{2} ) = log_{2}(1) = 0$

$sqrt{ {25}^{ frac{1}{ log_{6}(5) } } + {49}^{ frac{1}{ log_{8}(7) } } } = sqrt{ {25}^{ log_{5}(6) } + {49}^{ log_{7}(8) } } = sqrt{ { ({5}^{2}) }^{ log_{5}(6) } + { ({7}^{2} )}^{ log_{7}(8) } } = sqrt{ { ({5}^{ log_{5}(6) }) }^{2} + { ({7}^{ log_{7}(8) } )}^{2}} = sqrt{ {6}^{2} + {8}^{2} } = sqrt{36 + 64} = sqrt{100} = 10$