ln(x-4)+ln(x+1)=ln(x+8)

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Solution for ln(x-4)+ln(x+1)=ln(x+8) equation: 


Simplifying
ln(x + -4) + ln(x + 1) = ln(x + 8)

Reorder the terms:
ln(-4 + x) + ln(x + 1) = ln(x + 8)
(-4 * ln + x * ln) + ln(x + 1) = ln(x + 8)
(-4ln + lnx) + ln(x + 1) = ln(x + 8)

Reorder the terms:
-4ln + lnx + ln(1 + x) = ln(x + 8)
-4ln + lnx + (1 * ln + x * ln) = ln(x + 8)
-4ln + lnx + (1ln + lnx) = ln(x + 8)

Reorder the terms:
-4ln + 1ln + lnx + lnx = ln(x + 8)

Combine like terms: -4ln + 1ln = -3ln
-3ln + lnx + lnx = ln(x + 8)

Combine like terms: lnx + lnx = 2lnx
-3ln + 2lnx = ln(x + 8)

Reorder the terms:
-3ln + 2lnx = ln(8 + x)
-3ln + 2lnx = (8 * ln + x * ln)
-3ln + 2lnx = (8ln + lnx)

Solving
-3ln + 2lnx = 8ln + lnx

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
-3ln + -8ln + 2lnx = 8ln + -8ln + lnx

Combine like terms: -3ln + -8ln = -11ln
-11ln + 2lnx = 8ln + -8ln + lnx

Combine like terms: 8ln + -8ln = 0
-11ln + 2lnx = 0 + lnx
-11ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-11ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-11ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-11ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-11 + 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 '(-11 + x)' equal to zero and attempt to solve:

Simplifying
-11 + x = 0

Solving
-11 + x = 0

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

Add '11' to each side of the equation.
-11 + 11 + x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + x = 0 + 11
x = 0 + 11

Combine like terms: 0 + 11 = 11
x = 11

Add '-1x' to each side of the equation.
x + -1x = 11 + -1x

Combine like terms: x + -1x = 0
0 = 11 + -1x

Simplifying
0 = 11 + -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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