ln(x+6)-ln(x-2)=ln(x)

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Solution for ln(x+6)-ln(x-2)=ln(x) equation: 


Simplifying
ln(x + 6) + -1ln(x + -2) = ln(x)

Reorder the terms:
ln(6 + x) + -1ln(x + -2) = ln(x)
(6 * ln + x * ln) + -1ln(x + -2) = ln(x)
(6ln + lnx) + -1ln(x + -2) = ln(x)

Reorder the terms:
6ln + lnx + -1ln(-2 + x) = ln(x)
6ln + lnx + (-2 * -1ln + x * -1ln) = ln(x)
6ln + lnx + (2ln + -1lnx) = ln(x)

Reorder the terms:
6ln + 2ln + lnx + -1lnx = ln(x)

Combine like terms: 6ln + 2ln = 8ln
8ln + lnx + -1lnx = ln(x)

Combine like terms: lnx + -1lnx = 0
8ln + 0 = ln(x)
8ln = ln(x)

Multiply ln * x
8ln = lnx

Solving
8ln = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
8ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
8ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Add 'x' to each side of the equation.
-1x + x = -8 + x

Combine like terms: -1x + x = 0
0 = -8 + x

Simplifying
0 = -8 + x

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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