Question

СРОЧНОООО! ЛОГАРИФМИ

Answer 1

$log_{64}( \sqrt[3]{2} ) = log_{ {2}^{6} }( {2}^{ \frac{1}{3} } ) = \frac{1}{6} \times \frac{1}{3} \times log_{2}(2) = \frac{1}{18}$

${10}^{2 lg(7) } = {10}^{ lg( {7}^{2} ) } = 49$

${27}^{1 - log_{3}(4) } = \frac{27}{ {27}^{ log_{3}(4) } } = \frac{27}{ {3}^{3 log_{ 3}(4) } } = = \frac{27}{ {3}^{ log_{3}( {4}^{3} ) } } = \frac{27}{ {4}^{3} } = \frac{27}{64}$

${5}^{ \frac{4}{ log_{3}(5) } } = {5}^{4 \times (1 \div \frac{1}{ log_{5}(3) }) } = {5}^{4 log_{5}(3) } = {5}^{ log_{5}( {3}^{4} ) } = {3}^{4} = 81$