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

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

Simplifying
2ln(1 + -1x) = ln(x + 5)
(1 * 2ln + -1x * 2ln) = ln(x + 5)
(2ln + -2lnx) = ln(x + 5)

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

Solving
2ln + -2lnx = 5ln + lnx

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.
2ln + -5ln + -2lnx = 5ln + -5ln + lnx

Combine like terms: 2ln + -5ln = -3ln
-3ln + -2lnx = 5ln + -5ln + lnx

Combine like terms: 5ln + -5ln = 0
-3ln + -2lnx = 0 + lnx
-3ln + -2lnx = lnx

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

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

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

Factor out the Greatest Common Factor (GCF), '-3ln'.
-3ln(1 + x) = 0

Ignore the factor -3.
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.