ln(2x-5)-ln(x-1)=0

Solution for ln(2x-5)-ln(x-1)=0 equation:

Simplifying
ln(2x + -5) + -1ln(x + -1) = 0

Reorder the terms:
ln(-5 + 2x) + -1ln(x + -1) = 0
(-5 * ln + 2x * ln) + -1ln(x + -1) = 0
(-5ln + 2lnx) + -1ln(x + -1) = 0

Reorder the terms:
-5ln + 2lnx + -1ln(-1 + x) = 0
-5ln + 2lnx + (-1 * -1ln + x * -1ln) = 0
-5ln + 2lnx + (1ln + -1lnx) = 0

Reorder the terms:
-5ln + 1ln + 2lnx + -1lnx = 0

Combine like terms: -5ln + 1ln = -4ln
-4ln + 2lnx + -1lnx = 0

Combine like terms: 2lnx + -1lnx = 1lnx
-4ln + 1lnx = 0

Solving
-4ln + 1lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-4 + 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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Add '-1x' to each side of the equation.
x + -1x = 4 + -1x

Combine like terms: x + -1x = 0
0 = 4 + -1x

Simplifying
0 = 4 + -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.