Question

Sobre logaritmos, calcule
log4 √2

Answer 1

Olá.

Propriedades usadas:

$\star~\boxed{\ell og_{a^n} b = \dfrac{1}{n}\ell og_a b}\\ \\ \\ \star ~\boxed{\ell og_a b^n = n\cdot \ell og_a b}$

Vamos lá:

$\ell og_4 \sqrt2 = \ell og_{2^2}\sqrt2 = \dfrac12\ell og_2 \sqrt2 = \dfrac{1}{2}\ell og_2 2^{\frac12} = \dfrac12\cdot\dfrac12\ell og_2 2=\\ \\ \\ = \dfrac14\ell og _2 2 = \dfrac{1}{4}$

Assim:

$\boxed{\ell og_4\sqrt2}$

Dúvidas? Comente :)