ln(8-x)=ln(3x-2)+ln(x+2)

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Solution for ln(8-x)=ln(3x-2)+ln(x+2) equation: 


Simplifying
ln(8 + -1x) = ln(3x + -2) + ln(x + 2)
(8 * ln + -1x * ln) = ln(3x + -2) + ln(x + 2)
(8ln + -1lnx) = ln(3x + -2) + ln(x + 2)

Reorder the terms:
8ln + -1lnx = ln(-2 + 3x) + ln(x + 2)
8ln + -1lnx = (-2 * ln + 3x * ln) + ln(x + 2)
8ln + -1lnx = (-2ln + 3lnx) + ln(x + 2)

Reorder the terms:
8ln + -1lnx = -2ln + 3lnx + ln(2 + x)
8ln + -1lnx = -2ln + 3lnx + (2 * ln + x * ln)
8ln + -1lnx = -2ln + 3lnx + (2ln + lnx)

Reorder the terms:
8ln + -1lnx = -2ln + 2ln + 3lnx + lnx

Combine like terms: -2ln + 2ln = 0
8ln + -1lnx = 0 + 3lnx + lnx
8ln + -1lnx = 3lnx + lnx

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

Solving
8ln + -1lnx = 4lnx

Solving for variable 'l'.

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

Add '-4lnx' to each side of the equation.
8ln + -1lnx + -4lnx = 4lnx + -4lnx

Combine like terms: -1lnx + -4lnx = -5lnx
8ln + -5lnx = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
8ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(8 + -5x) = 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 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 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 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Add '5x' to each side of the equation.
-5x + 5x = -8 + 5x

Combine like terms: -5x + 5x = 0
0 = -8 + 5x

Simplifying
0 = -8 + 5x

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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