ln×+ln(×-2)=1

Question

Logarithms

Answer 1

ln×+ln(×-2)=1

ln{x(x-2)} = 1

ln{x(x-2)} = ln(e)

x(x - 2) = e

x^2 - 2x - e = 0

Now use the quadratic formula, x = (-b +/- sqrt(b^2 - 4ac))/(2a), where a = 1, b = -2, c = -e.

i.e. x = (2 +/- sqrt(4 - 4*1*(-e))) / (2*1)

x = (2 +/- 2*sqrt(1 + e)) / 2

x = 1 +/- sqrt(1 + e)