Question

log de um quarto na base 2

Answer 1

$1/a^{n}=a^{-n}$
$log_{b}(a^{n})=n*log_{b}(a)$
$log_{x}(x)=1$
_____________________

$log_{2}(1/4) = log_{2}(1/2^{2})$
$log_{2}(1/4)=log_{2}(2^{-2})$
$log_{2}(1/4)=(-2)*log_{2}(2)$
$log_{2}(1/4)=(-2)*1$
$log_{2}(1/4)=-2$

Answer 2

$log_{2}\frac{1}{4}$

Pela teoria:

$log_{2}\frac{1}{4} = x \\\\ 2^{x} = \frac{1}{4} \\\\ 2^{x} = \frac{1}{4}$

Podemos inverter o numerador com o denominador, para isso, basta trocar o sinal do expoente da fração:

$2^{x} = (\frac{1}{4})^{1} \\\\ 2^{x} = (\frac{4}{1})^{-1} \\\\ 2^{x} = (4)^{-1} \\\\ 2^{x} = (2^{2})^{-1} \\\\ 2^{x} = 2^{-2} \\\\ \not{2}^{x} = \not{2}^{-2} \\\\ \boxed{x = -2}$


$\therefore \boxed{\boxed{log_{2}\frac{1}{4} = -2}}$