Question

sendo log 2 na base x = a, log 3 na base de x = b, determine log raiz cubica de 12 na base x

Answer 1

$log_{x} 2 = a$
$log_{x} 3 = b$

$log_{x} \sqrt[3]{12} \\ log_{x}12^{ \frac{1}{3} } \\ \frac{1}{3}log_{x} 12 \\ \frac{1}{3}log_{x} (2*2*3)\\ \frac{1}{3}(log_{x}2 + log_{x}2 + log_{x}3) \\ \frac{1}{3} (a+a+b) \\ \frac{1}{3} (2a+b) \\ \frac{2a}{3} + \frac{b}{3} = \frac{2a+b}{3}$