Question

A solução de log5 (x+2)- log5 x=1 é:


a) 4
b)1/4
c)1/2
d) 1/3
e)8

Answer 1

log5 (x+2) - log5 x = 1
log5 (x+2)/x = 1
5¹ = (x+2)/x
5x = x+ 2
5x - x = 2
4x = 2
x = 2/4
x = 1/2

Resposta: x = 1/2 - alternativa C)

Espero ter ajudado.

Answer 2

$\log_5(x+2)-\log_5x=1\\\\\log_5\left[\dfrac{x+2}{x}\right]=1\Longleftrightarrow5^{1}=\dfrac{x+2}{x}\\\\\\5=\dfrac{x+2}{x}\\\\\\5x=x+2\\\\4x=2\\\\x=\dfrac{2}{4}\\\\\\x=\dfrac{1}{2}\\\\\\\boxed{S=\left\{\dfrac{1}{2}\right\}}\\\\\\\text{Alternativa c).}$