ln(x-1)+ln(x-1)-2ln(x)-1=0

Solution for ln(x-1)+ln(x-1)-2ln(x)-1=0 equation:

Simplifying
ln(x + -1) + ln(x + -1) + -2ln(x) + -1 = 0

Reorder the terms:
ln(-1 + x) + ln(x + -1) + -2ln(x) + -1 = 0
(-1 * ln + x * ln) + ln(x + -1) + -2ln(x) + -1 = 0
(-1ln + lnx) + ln(x + -1) + -2ln(x) + -1 = 0

Reorder the terms:
-1ln + lnx + ln(-1 + x) + -2ln(x) + -1 = 0
-1ln + lnx + (-1 * ln + x * ln) + -2ln(x) + -1 = 0
-1ln + lnx + (-1ln + lnx) + -2ln(x) + -1 = 0

Multiply ln * x
-1ln + lnx + -1ln + lnx + -2lnx + -1 = 0

Reorder the terms:
-1 + -1ln + -1ln + lnx + lnx + -2lnx = 0

Combine like terms: -1ln + -1ln = -2ln
-1 + -2ln + lnx + lnx + -2lnx = 0

Combine like terms: lnx + lnx = 2lnx
-1 + -2ln + 2lnx + -2lnx = 0

Combine like terms: 2lnx + -2lnx = 0
-1 + -2ln + 0 = 0
-1 + -2ln = 0

Solving
-1 + -2ln = 0

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -2ln = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2ln = 0 + 1
-2ln = 0 + 1

Combine like terms: 0 + 1 = 1
-2ln = 1

Divide each side by '-2n'.
l = -0.5n-1

Simplifying
l = -0.5n-1