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

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

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

Reorder the terms:
2ln(2 + x) = ln(x + 3)
(2 * 2ln + x * 2ln) = ln(x + 3)
(4ln + 2lnx) = ln(x + 3)

Reorder the terms:
4ln + 2lnx = ln(3 + x)
4ln + 2lnx = (3 * ln + x * ln)
4ln + 2lnx = (3ln + lnx)

Solving
4ln + 2lnx = 3ln + lnx

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.
4ln + -3ln + 2lnx = 3ln + -3ln + lnx

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

Combine like terms: 3ln + -3ln = 0
1ln + 2lnx = 0 + lnx
1ln + 2lnx = lnx

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

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

Combine like terms: lnx + -1lnx = 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.