Question

logaritmos, ajuda pls

Answer 1

Explicação passo-a-passo:

Boa tarde, vamos aplicar as propriedades dos logaritmos na expressão:

$log_{a}( \frac{ \sqrt[3]{36} }{1.5} ) = log_{a}( \sqrt[3]{36} ) - log_{a}(1.5)$

$= log_{a}( \sqrt[3]{ {6}^{2} } ) - log_{a}( \frac{3}{2} )$

$= log_{a}( {6}^{ \frac{2}{3} } ) - ( log_{a}(3) - log_{a}(2) )$

$= \frac{2}{3} log_{a}(3 \times 2) - (y - x)$

$= \frac{2}{3} ( log_{a}(3) + log_{a}(2) ) - (y - x)$

$= \frac{2}{3} (y + x) - (y - x)$

$= \frac{2}{3} y + \frac{2}{3} x - \frac{3}{3} y + \frac{3}{3} x$

$= - \frac{1}{3} y + \frac{5}{3} x$