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

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


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

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

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

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

Combine like terms: 3ln + 2ln = 5ln
5ln + lnx + -1lnx = ln(2x)

Combine like terms: lnx + -1lnx = 0
5ln + 0 = ln(2x)
5ln = ln(2x)

Remove parenthesis around (2x)
5ln = ln * 2x

Reorder the terms for easier multiplication:
5ln = 2ln * x

Multiply ln * x
5ln = 2lnx

Solving
5ln = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
5ln + -2lnx = 2lnx + -2lnx

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -2x) = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Add '2x' to each side of the equation.
-2x + 2x = -5 + 2x

Combine like terms: -2x + 2x = 0
0 = -5 + 2x

Simplifying
0 = -5 + 2x

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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