Question

A solução real da equação logarítmica -1 = log 5 [ 2x/(x + 1) ] é:

Answer 1

Explicação passo-a-passo:

$\sf -1=log_{5}~\Big(\dfrac{2x}{x+1}\Big)$

$\sf \dfrac{2x}{x+1}=5^{-1}$

$\sf \dfrac{2x}{x+1}=\dfrac{1}{5}$

$\sf 5\cdot2x=(x+1)\cdot1$

$\sf 10x=x+1$

$\sf 10x-x=1$

$\sf 9x=1$

$\sf \red{x=\dfrac{1}{9}}$

Answer 2

Oie, Td Bom?!

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

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

$\frac{2x}{x + 1} = 5 {}^{ - 1}$

$\frac{2x}{x + 1} = \frac{1}{5}$

$5 \: . \: 2x = 1(x + 1)$

$10x = x + 1$

$10x - x = 1$

$9x = 1$

$x = \frac{1}{9}$

Att. Makaveli1996