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

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


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

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

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

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

Combine like terms: 2lnx + -2lnx = 0
-2ln + lnx = 3ln + 0
-2ln + lnx = 3ln

Solving
-2ln + lnx = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-2ln + -3ln + lnx = 3ln + -3ln

Combine like terms: -2ln + -3ln = -5ln
-5ln + lnx = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-5ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + 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 '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Add '-1x' to each side of the equation.
x + -1x = 5 + -1x

Combine like terms: x + -1x = 0
0 = 5 + -1x

Simplifying
0 = 5 + -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.

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