ln(2x+1)-ln(x-3)=ln(5)

Solution for ln(2x+1)-ln(x-3)=ln(5) equation:

Simplifying
ln(2x + 1) + -1ln(x + -3) = ln(5)

Reorder the terms:
ln(1 + 2x) + -1ln(x + -3) = ln(5)
(1 * ln + 2x * ln) + -1ln(x + -3) = ln(5)
(1ln + 2lnx) + -1ln(x + -3) = ln(5)

Reorder the terms:
1ln + 2lnx + -1ln(-3 + x) = ln(5)
1ln + 2lnx + (-3 * -1ln + x * -1ln) = ln(5)
1ln + 2lnx + (3ln + -1lnx) = ln(5)

Reorder the terms:
1ln + 3ln + 2lnx + -1lnx = ln(5)

Combine like terms: 1ln + 3ln = 4ln
4ln + 2lnx + -1lnx = ln(5)

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

Reorder the terms for easier multiplication:
4ln + 1lnx = 5ln

Solving
4ln + 1lnx = 5ln

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
4ln + -5ln + 1lnx = 5ln + -5ln

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

Combine like terms: 5ln + -5ln = 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.