Question

19)calculem :
$log_{3}(5) \times log_{4}(27) \times log_{25}( \sqrt{2} )$
porfavor resposta com cálculo! ​

Answer 1

Explicação passo-a-passo:

$log_{3}(5) \times log_{4}(27) \times log_{25}( \sqrt{2} ) \\ log_{3}(5) \times \frac{1}{ log_{ {3}^{3} }(4) } \times log_{ {5}^{2} }( \sqrt{2} ) \\ log_{ 3}(5) \times \frac{1}{ \frac{1}{3} log_{3}(4) } \times \frac{1}{2} log_{5}( \sqrt{2} ) \\ \\ \frac{ log_{3}(5) }{ log_{3}( \sqrt[3]{4} ) } \times log_{5}( \sqrt[4]{2} ) \\ log_{ \sqrt[ 3]{4} }(5) \times log_{5}( \sqrt[4]{2} ) \\ \\ \frac{ log_{5}( \sqrt[4]{2} ) }{ log_{5}( \sqrt[3]{4} ) } = log_{ \sqrt[3]{4} }( \sqrt[4]{2} ) \\ 3 log_{4}( {2}^{ \frac{1}{4} } ) \\ log_{4}( \sqrt[4]{ {2}^{3} } )$

Espero ter lhe ajudado! ☺✌