ln(x)+ln(x+6)=ln(13/4)

Solution for ln(x)+ln(x+6)=ln(13/4) equation:

D( x )

x <= 0

x+6 <= 0

x <= 0

x+6 <= 0

x+6 <= 0

x+6 <= 0 // - 6

x <= -6

x in (0:+oo)

ln(x)+ln(x+6) = ln(13/4) // - ln(13/4)

ln(x)+ln(x+6)-ln(13/4) = 0

ln(1*x)+ln(x+6)-ln(13/4) = 0

ln(1*x*(x+6))-ln(13/4) = 0

ln(1*x*(x+6))+ln(1/13/4) = 0

ln(1*x*(x+6))+ln(4/13) = 0 // - ln(4/13)

ln(1*x*(x+6)) = -ln(4/13)

1*x*(x+6) = 1/4/13

1*x*(x+6)-(1/4/13) = 0

x*(x+6)-13/4 = 0

(4*x*(x+6))/4-13/4 = 0

4*x*(x+6)-13 = 0

4*x^2+24*x-13 = 0

4*x^2+24*x-13 = 0

4*x^2+24*x-13 = 0

DELTA = 24^2-(-13*4*4)

DELTA = 784

DELTA > 0

x = (784^(1/2)-24)/(2*4) or x = (-784^(1/2)-24)/(2*4)

x = 1/2 or x = -13/2

(x+13/2)*(x-1/2) = 0

((x+13/2)*(x-1/2))/4 = 0

((x+13/2)*(x-1/2))/4 = 0 // * 4

(x+13/2)*(x-1/2) = 0

( x+13/2 )

x+13/2 = 0 // - 13/2

x = -13/2

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

x in { -13/2} 

x = 1/2