Question

log4(8.
$\sqrt[3]{2}$
)​

Answer 1

Resposta:

Explicação passo-a-passo:

$log4(8 *\sqrt[3]{2}) = log4(2^3*2^{\frac{1}{3}}) = log4(2^{3+\frac{1}{3}}) = log4(2^{\frac{10}{3}}) = log4(2^\frac{10}{3}) \\ \\log4(2^\frac{10}{3})= x\\4^x =2^\frac{10}{3}\\(2^2)^x= 2^\frac{10}{3}\\\\2^{2x}=2^\frac{10}{3}\\\\2x= \frac{10}{3}\\\\x= \frac{10}{6} =  \frac{5}{3}$

Answer 2

Explicação passo-a-passo:

$\log_48\sqrt[3]{2} =x\\ \\ 4^x=8.2^{{1\over3}}\\ \\ 4^x=2^3.2^{{1\over3}}\\ \\ 2^{2x}=2^{{9+1\over3}}\\ \\ 2^{2x}=2^{{10\over3}}\\ \\ cancela~~ 2\\ \\ 2x={10\over3}\\ \\ 6x=10\\ \\ x={10\over6}={5\over3}\\ \\ Logo\\ \\ \log_48\sqrt[3]{2} ={5\over3}$