Question

O valor de log4(8 . ∛2), alguem pode me ajudar a resolver?

Answer 1

$\sqrt[n]{a^{x}}= a^{x/n}$
$a^{x}*a^{y}=a^{(x+y)}$

$log_{(b^{n})}(a)=(1/n)*log_{b}(a)$
$log_{b}(a^{n})=n*log_{b}(a)$
$log_{n}(n)=1$
__________________________

$log_{4}(8 * \sqrt[3]{2}) = log_{(2^{2})}(2^{3} * 2^{1/3})$
$log_{4}(8 * \sqrt[3]{2}) = (1 / 2)*log_{2}(2^{(3 + [1/3])})$
$log_{4}(8 * \sqrt[3]{2}) = (1 / 2)*log_{2}(2^{10/3})$
$log_{4}(8 * \sqrt[3]{2}) = (1 / 2)*(10/3)*log_{2}(2)$
$log_{4}(8 * \sqrt[3]{2}) = (1 / 1)*(5/3)*1$
$log_{4}(8 * \sqrt[3]{2}) = 5/3$