Question

Qual o nºreal x que satisfaz a equação log4(10-4x)=2 ??

Answer 1

Resposta:

$\text{\sf Leia abaixo}$

Explicação passo-a-passo:

$\sf log_4\:(10-4x) = 2$

$\sf \not log_4\:(10-4x) = \not log_4\:16$

$\sf 10 - 4x = 16$

$\sf 4x = 10 - 16$

$\sf 4x = -6$

$\boxed{\boxed{\sf x = -\dfrac{3}{2}}}$

Answer 2

Oie, Td Bom?!

$log_{4}(10 - 4x) = 2$

$log_{4}(2(5 - 2x)) = 2$

$log_{4}(2) + log_{4}(5 - 2x) = 2$

$log_{2 {}^{2} }(4) + log_{4}(5 - 2x) = 2$

$\frac{1}{2} \: . \: log_{2}(2) + log_{4}(5 - 2x) = 2$

$\frac{1}{2} \: . \: 1 + log_{4}(5 - 2x) = 2$

$\frac{1}{2} + log_{4}(5 - 2x) = 2$

$log_{4}(5 - 2x) = 2 - \frac{1}{2}$

$log_{4}(5 - 2x) = \frac{3}{2}$

$5 - 2x = 4 {}^{ \frac{3}{2} }$

$5 - 2x = (2 {}^{2} ) {}^{ \frac{3}{2} }$

$5 - 2x = 2 {}^{3}$

$5 - 2x = 8$

$- 2x = 8 - 5$

$- 2x = 3$

$x = - \frac{3}{2}$

Att. Makaveli1996