ln(x+1)+ln(x-5)=ln(13)

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Solution for ln(x+1)+ln(x-5)=ln(13) equation:


Simplifying
ln(x + 1) + ln(x + -5) = ln(13)

Reorder the terms:
ln(1 + x) + ln(x + -5) = ln(13)
(1 * ln + x * ln) + ln(x + -5) = ln(13)
(1ln + lnx) + ln(x + -5) = ln(13)

Reorder the terms:
1ln + lnx + ln(-5 + x) = ln(13)
1ln + lnx + (-5 * ln + x * ln) = ln(13)
1ln + lnx + (-5ln + lnx) = ln(13)

Reorder the terms:
1ln + -5ln + lnx + lnx = ln(13)

Combine like terms: 1ln + -5ln = -4ln
-4ln + lnx + lnx = ln(13)

Combine like terms: lnx + lnx = 2lnx
-4ln + 2lnx = ln(13)

Reorder the terms for easier multiplication:
-4ln + 2lnx = 13ln

Solving
-4ln + 2lnx = 13ln

Solving for variable 'l'.

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

Add '-13ln' to each side of the equation.
-4ln + -13ln + 2lnx = 13ln + -13ln

Combine like terms: -4ln + -13ln = -17ln
-17ln + 2lnx = 13ln + -13ln

Combine like terms: 13ln + -13ln = 0
-17ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-17 + 2x) = 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 '(-17 + 2x)' equal to zero and attempt to solve: Simplifying -17 + 2x = 0 Solving -17 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 2x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2x = 0 + 17 2x = 0 + 17 Combine like terms: 0 + 17 = 17 2x = 17 Add '-2x' to each side of the equation. 2x + -2x = 17 + -2x Combine like terms: 2x + -2x = 0 0 = 17 + -2x Simplifying 0 = 17 + -2x 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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