Find the value of x in: log (x+4) - log (x+2) = log x?

log [ (x + 4) / (x + 2) ] = log x
(x + 4) / (x + 2) = x
x + 4 = x ² + 2 x
x ² + x - 4 = 0
x = [ - 1 ± √ (1 + 16) ] / 2
x = [ - 1 ± √ (17) ] / 2

(x+4)/(x+2) = x

x + 4 = x^2 + 2x

x^2 + x -4 = 0

find x value by using quadratic formula.

(x+4)/(x+2) = x

1 + 2/(x+2) = x

2/(x+2) = x -1

2 = (x-1)(x+2)

the rest is ez

=> (x+4)/(x+2)=x
x+4= x²+2x
x²+x-4=0
D= 15
x1= (-1+sqrt(15))/2
x2=(-1- sqrt(15))/2