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

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


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

Reorder the terms:
2ln(2 + x) = ln(x + -1)
(2 * 2ln + x * 2ln) = ln(x + -1)
(4ln + 2lnx) = ln(x + -1)

Reorder the terms:
4ln + 2lnx = ln(-1 + x)
4ln + 2lnx = (-1 * ln + x * ln)
4ln + 2lnx = (-1ln + lnx)

Solving
4ln + 2lnx = -1ln + lnx

Solving for variable 'l'.

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

Add 'ln' to each side of the equation.
4ln + ln + 2lnx = -1ln + ln + lnx

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

Combine like terms: -1ln + ln = 0
5ln + 2lnx = 0 + lnx
5ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
5ln + 2lnx + -1lnx = lnx + -1lnx

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

Combine like terms: lnx + -1lnx = 0
5ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Add '-1x' to each side of the equation.
x + -1x = -5 + -1x

Combine like terms: x + -1x = 0
0 = -5 + -1x

Simplifying
0 = -5 + -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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