Question 668792
ln(x) + ln(x+3) = 1

ln(x*(x+3) = 1

e^(ln(x*(x+3)) = e^1

x^2 + 3x = e

x^2 +3x -e = 0

By quadratic formula you get x = {{{(1/2)sqrt(9+4e) -3}}} = .729 as the only positive solution. Since ln(x) where x is negative is undefined.

ln(x+1) - ln(x-2) = ln(x^2)

ln((x+1)/(x-2)) = ln(x^2)

e^ln((x+1)/(x-2)) = e^ln(x^2)

(x+1)/(x-2) = x^2

x+1 = x^3 - 2x^2

x^3 -2x^2 -x -1 = 0

Find that x = 2.55 is the only real solution.