ln(x+2)+ln(x/3)=0

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Solution for ln(x+2)+ln(x/3)=0 equation: 


D( x )

x/3 <= 0

x+2 <= 0

x/3 <= 0

x/3 <= 0

1/3*x+0 <= 0 // - 0

1/3*x <= 0 // : 1/3

x <= 0/1/3

x <= 0

x+2 <= 0

x+2 <= 0

x+2 <= 0 // - 2

x <= -2

x in (0:+oo)

ln(x+2)+ln(x/3) = 0

ln(1*(x+2))+ln(x/3) = 0

ln(1*(x/3)*(x+2)) = 0

ln((x/3)*(x+2)) = 0

ln((x/3)*(x+2)) = ln(e^0)

(x/3)*(x+2) = e^0

(x/3)*(x+2)-e^0 = 0

1/3*x*(x+2)-1 = 0

1/3*x*(x+2)-1 = 0

1/3*x^2+2/3*x-1 = 0

1/3*x^2+2/3*x-1 = 0

1/3*x^2+2/3*x-1 = 0

DELTA = (2/3)^2-(-1*1/3*4)

DELTA = 16/9

DELTA > 0

x = ((16/9)^(1/2)-2/3)/(1/3*2) or x = (-(16/9)^(1/2)-2/3)/(1/3*2)

x = 1 or x = -3

(x+3)*(x-1) = 0

(x+3)*(x-1) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -3} 

x = 1

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