Logaritmos

por **Souo** » Sáb Jun 20, 2015 15:26

Se log a=3 e log b=1, ent?o o log $\sqrt[3]{\frac{a}{{B}^{2}}}$

A) 1
B) 1/3
C) 2/3
D) -1
E) -1/3

por **DanielFerreira** » Dom Jun 21, 2015 18:02

Olá Souo, boa tarde!

$\\ \log \sqrt[3]{\frac{a}{b^2}} = \\\\ \log \left ( \frac{a}{b^2} \right )^{\frac{1}{3}} = \\\\ \frac{1}{3} \cdot \log \left ( \frac{a}{b^2} \right ) = \\\\ \frac{1}{3} \cdot (\log a - \log b^2) = \\\\ \frac{\log a - 2 \cdot \log b}{3} = \\\\ \frac{3 - 2 \cdot 1}{3} = \\\\ \boxed{\frac{1}{3}}$

Logaritmos

Logaritmos

Logaritmos

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