Question

resolva a equação log4²(x)-2log4(x)-3=0 um​

Answer 1

Resposta:

X=1/32

Explicação passo-a-passo:

$log_{4}(2x) - 2 log_{4}(x ) - 3 = 0 \\ \\ log_{ {2}^{2} }(2x) - 2 log_{ {2}^{2} }(x ) - 3 = 0 \\ \\ \dfrac{1}{2} log_{ 2 }(2x) - \dfrac{2}{2} log_{ 2 }(x ) - 3 = 0 \\ \\ \dfrac{1}{2} log_{ 2 }(2) + \dfrac{1}{2} log_{ 2 }(x)- \dfrac{2}{2} log_{ 2 }(x ) - 3 = 0 \\ \\ + \dfrac{1}{2} log_{ 2 }(x)- log_{ 2 }(x ) = 0 - \dfrac{1}{2} + 3 \\ \\ (\dfrac{1}{2} - 1) log_{ 2 }(x)= 0 - \dfrac{1}{2} + 3 \\ \\ - \dfrac{1}{2} log_{ 2 }(x)= \dfrac{5}{2} \\ \\ log_{ 2 }(x)= \dfrac{ \frac{5}{2} }{ - \frac{1}{2} } \\ \\ log_{ 2 }(x) = -5 \\ \\ {2}^{-5} =x \\ \\ \boxed{\boxed{X=\dfrac{1}{32}}}$