ln(x-3)-ln(2x-1)=1

Solution for ln(x-3)-ln(2x-1)=1 equation:

Simplifying
ln(x + -3) + -1ln(2x + -1) = 1

Reorder the terms:
ln(-3 + x) + -1ln(2x + -1) = 1
(-3 * ln + x * ln) + -1ln(2x + -1) = 1
(-3ln + lnx) + -1ln(2x + -1) = 1

Reorder the terms:
-3ln + lnx + -1ln(-1 + 2x) = 1
-3ln + lnx + (-1 * -1ln + 2x * -1ln) = 1
-3ln + lnx + (1ln + -2lnx) = 1

Reorder the terms:
-3ln + 1ln + lnx + -2lnx = 1

Combine like terms: -3ln + 1ln = -2ln
-2ln + lnx + -2lnx = 1

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

Solving
-2ln + -1lnx = 1

Solving for variable 'l'.

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 2ln + lnx) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 2ln + lnx)' equal to zero and attempt to solve:

Simplifying
1 + 2ln + lnx = 0

Solving
1 + 2ln + lnx = 0

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

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

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

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

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

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.