ln(x)+ln(x+4)=ln(33/4)

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Solution for ln(x)+ln(x+4)=ln(33/4) equation: 


D( x )

x <= 0

x+4 <= 0

x <= 0

x+4 <= 0

x+4 <= 0

x+4 <= 0 // - 4

x <= -4

x in (0:+oo)

ln(x)+ln(x+4) = ln(33/4) // - ln(33/4)

ln(x)+ln(x+4)-ln(33/4) = 0

ln(1*x)+ln(x+4)-ln(33/4) = 0

ln(1*x*(x+4))-ln(33/4) = 0

ln(1*x*(x+4))+ln(1/33/4) = 0

ln(1*x*(x+4))+ln(4/33) = 0 // - ln(4/33)

ln(1*x*(x+4)) = -ln(4/33)

1*x*(x+4) = 1/4/33

1*x*(x+4)-(1/4/33) = 0

x*(x+4)-33/4 = 0

(4*x*(x+4))/4-33/4 = 0

4*x*(x+4)-33 = 0

4*x^2+16*x-33 = 0

4*x^2+16*x-33 = 0

4*x^2+16*x-33 = 0

DELTA = 16^2-(-33*4*4)

DELTA = 784

DELTA > 0

x = (784^(1/2)-16)/(2*4) or x = (-784^(1/2)-16)/(2*4)

x = 3/2 or x = -11/2

(x+11/2)*(x-3/2) = 0

((x+11/2)*(x-3/2))/4 = 0

((x+11/2)*(x-3/2))/4 = 0 // * 4

(x+11/2)*(x-3/2) = 0

( x+11/2 )

x+11/2 = 0 // - 11/2

x = -11/2

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

x in { -11/2} 

x = 3/2

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