solve the equation

Question

Inx+In(x+4)=3

x= ?

Answer 1

Use the property :
ln (AB) = lnA + lnB

lnx + ln(x+4) = 3 , where x > 0
ln [x(x+4)} = 3
x(x+4) = e^3
x^2 + 4x = e^3

completing the square, rather than using the formula

x^2 + 4x + 4 = e^3 + 4
(x+2)^2 = e^3 + 4

x+2 = ± √(e^3 + 4)

x = -2 ± √(e^3 + 4) , but since x > 0

x = -2 + √(e^3 + 4) or appr 2.9077