ln(x+1)+ln(x-8)=ln(-5x)

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Solution for ln(x+1)+ln(x-8)=ln(-5x) equation:


Simplifying
ln(x + 1) + ln(x + -8) = ln(-5x)

Reorder the terms:
ln(1 + x) + ln(x + -8) = ln(-5x)
(1 * ln + x * ln) + ln(x + -8) = ln(-5x)
(1ln + lnx) + ln(x + -8) = ln(-5x)

Reorder the terms:
1ln + lnx + ln(-8 + x) = ln(-5x)
1ln + lnx + (-8 * ln + x * ln) = ln(-5x)
1ln + lnx + (-8ln + lnx) = ln(-5x)

Reorder the terms:
1ln + -8ln + lnx + lnx = ln(-5x)

Combine like terms: 1ln + -8ln = -7ln
-7ln + lnx + lnx = ln(-5x)

Combine like terms: lnx + lnx = 2lnx
-7ln + 2lnx = ln(-5x)

Remove parenthesis around (-5x)
-7ln + 2lnx = ln * -5x

Reorder the terms for easier multiplication:
-7ln + 2lnx = -5ln * x

Multiply ln * x
-7ln + 2lnx = -5lnx

Solving
-7ln + 2lnx = -5lnx

Solving for variable 'l'.

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

Add '5lnx' to each side of the equation.
-7ln + 2lnx + 5lnx = -5lnx + 5lnx

Combine like terms: 2lnx + 5lnx = 7lnx
-7ln + 7lnx = -5lnx + 5lnx

Combine like terms: -5lnx + 5lnx = 0
-7ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), '7ln'.
7ln(-1 + x) = 0

Ignore the factor 7.

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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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