ln(2x+1)=ln(x-4)

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Solution for ln(2x+1)=ln(x-4) equation: 


Simplifying
ln(2x + 1) = ln(x + -4)

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

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

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

Solving for variable 'l'.

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

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

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

Combine like terms: -4ln + 4ln = 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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