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

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


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

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

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

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

Solving
1ln + 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.
1ln + -3ln + lnx = 3ln + -3ln

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

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

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

Simplifying
-2 + x = 0

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

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

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

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

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

Simplifying
0 = 2 + -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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