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

lnx + ln (x+3) = 1
ln x(x+3) = 1
x(x+3) = e^1
x^2+3x = e^1
x^2+3x-e = 0
x^2+3x-2.7183 = 0

compare with ax^2+bx+c

a=1,b=3,c=-2.7183

discriminant
{{{x=(-b+-sqrt(b^2-4*a*c))/(2*a)}}}
                                                                                    

 calculate b^2-4ac
we get:
x= {0.728968371242625, -3.72896837124262}
Ignore negative value
x = 0.729


ln(x+1) - ln(x -2) a
={{{ ln ((x+1)/ (x-2))}}} 

we have.

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

x+1
____ = x^2
x -2 

cross multiply

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

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

The only way I know is to graph it ..