Question

sendo log x2- a, log x3- b , calcule logx $\sqrt[3]{12}$

Answer 1

Explicação passo-a-passo:

Sendo:

$log_{x}(2) = a \\ log_{x}(3) = b$

Temos:

$= log_{x}( \sqrt[3]{12} )$

$= log_{x}( {12}^{ \frac{1}{3} } )$

$= \frac{1}{3} log_{x}(12)$

$= \frac{1}{3} log_{x}(2 \times 2 \times 3)$

$= \frac{1}{3} ( log_{x}(2) + log_{x}(2) + log_{x}(3) )$

$= \frac{1}{3} (a + a + b)$

$= \frac{1}{3} (2a + b)$