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

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

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

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

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

Solving
3ln + lnx = 1ln + 2lnx

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
3ln + -1ln + lnx = 1ln + -1ln + 2lnx

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Add 'x' to each side of the equation.
-1x + x = -2 + x

Combine like terms: -1x + x = 0
0 = -2 + x

Simplifying
0 = -2 + x

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.