Question

Ln x + ln (x-3)=1 solve for x

Answer 1

x = 1.5 +√(e+2.25) ≈ 3.728964

Explanation:

Taking the antilog, you have ...

x(x -3) = e

x^2 -3x = e

x^2 -3x +2.25 = e+2.25 . . . . . add (3/2)^2 to complete the square

(x -1.5)^2 = e +2.25 . . . . . . . . . write as a square

x -1.5 = √(e +2.25) . . . . . . . . . only the positive square root is a solution

x = 1.5 +√(e+2.25) ≈ 3.728964