ln(x^2+8)-ln(x+1)=ln(x+2)

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Solution for ln(x^2+8)-ln(x+1)=ln(x+2) equation: 


Simplifying
ln(x2 + 8) + -1ln(x + 1) = ln(x + 2)

Reorder the terms:
ln(8 + x2) + -1ln(x + 1) = ln(x + 2)
(8 * ln + x2 * ln) + -1ln(x + 1) = ln(x + 2)
(8ln + lnx2) + -1ln(x + 1) = ln(x + 2)

Reorder the terms:
8ln + lnx2 + -1ln(1 + x) = ln(x + 2)
8ln + lnx2 + (1 * -1ln + x * -1ln) = ln(x + 2)
8ln + lnx2 + (-1ln + -1lnx) = ln(x + 2)

Reorder the terms:
8ln + -1ln + -1lnx + lnx2 = ln(x + 2)

Combine like terms: 8ln + -1ln = 7ln
7ln + -1lnx + lnx2 = ln(x + 2)

Reorder the terms:
7ln + -1lnx + lnx2 = ln(2 + x)
7ln + -1lnx + lnx2 = (2 * ln + x * ln)
7ln + -1lnx + lnx2 = (2ln + lnx)

Solving
7ln + -1lnx + lnx2 = 2ln + lnx

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
7ln + -1lnx + -2ln + lnx2 = 2ln + -2ln + lnx

Reorder the terms:
7ln + -2ln + -1lnx + lnx2 = 2ln + -2ln + lnx

Combine like terms: 7ln + -2ln = 5ln
5ln + -1lnx + lnx2 = 2ln + -2ln + lnx

Combine like terms: 2ln + -2ln = 0
5ln + -1lnx + lnx2 = 0 + lnx
5ln + -1lnx + lnx2 = lnx

Add '-1lnx' to each side of the equation.
5ln + -1lnx + -1lnx + lnx2 = lnx + -1lnx

Combine like terms: -1lnx + -1lnx = -2lnx
5ln + -2lnx + lnx2 = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
5ln + -2lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -2x + x2) = 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 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -2x + x2 = 0

Solving
5 + -2x + x2 = 0

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

Add '-5' to each side of the equation.
5 + -2x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -2x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x + x2 = 0 + -5
-2x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2x + x2 = -5

Add '2x' to each side of the equation.
-2x + 2x + x2 = -5 + 2x

Combine like terms: -2x + 2x = 0
0 + x2 = -5 + 2x
x2 = -5 + 2x

Add '-1x2' to each side of the equation.
x2 + -1x2 = -5 + 2x + -1x2

Combine like terms: x2 + -1x2 = 0
0 = -5 + 2x + -1x2

Simplifying
0 = -5 + 2x + -1x2

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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