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

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

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

Multiply ln * x
lnx + ln(x + -1) = ln(x + -2) + ln(2)

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

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

Combine like terms: lnx + lnx = 2lnx
-1ln + 2lnx = ln(x + -2) + ln(2)

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

Reorder the terms for easier multiplication:
-1ln + 2lnx = -2ln + lnx + 2ln

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

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

Solving
-1ln + 2lnx = lnx

Solving for variable 'l'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + x) = 0

Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Add '-1x' to each side of the equation.
x + -1x = 1 + -1x

Combine like terms: x + -1x = 0
0 = 1 + -1x

Simplifying
0 = 1 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.