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

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


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

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

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

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

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

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

Solving
1ln + 2lnx = 8ln + -2lnx

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.
1ln + -8ln + 2lnx = 8ln + -8ln + -2lnx

Combine like terms: 1ln + -8ln = -7ln
-7ln + 2lnx = 8ln + -8ln + -2lnx

Combine like terms: 8ln + -8ln = 0
-7ln + 2lnx = 0 + -2lnx
-7ln + 2lnx = -2lnx

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

Combine like terms: 2lnx + 2lnx = 4lnx
-7ln + 4lnx = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
-7ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + 4x) = 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 '(-7 + 4x)' equal to zero and attempt to solve: Simplifying -7 + 4x = 0 Solving -7 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 4x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4x = 0 + 7 4x = 0 + 7 Combine like terms: 0 + 7 = 7 4x = 7 Add '-4x' to each side of the equation. 4x + -4x = 7 + -4x Combine like terms: 4x + -4x = 0 0 = 7 + -4x Simplifying 0 = 7 + -4x 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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