ln(x+5)-ln(x+1)=ln(x-2)

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Solution for ln(x+5)-ln(x+1)=ln(x-2) equation:


Simplifying
ln(x + 5) + -1ln(x + 1) = ln(x + -2)

Reorder the terms:
ln(5 + x) + -1ln(x + 1) = ln(x + -2)
(5 * ln + x * ln) + -1ln(x + 1) = ln(x + -2)
(5ln + lnx) + -1ln(x + 1) = ln(x + -2)

Reorder the terms:
5ln + lnx + -1ln(1 + x) = ln(x + -2)
5ln + lnx + (1 * -1ln + x * -1ln) = ln(x + -2)
5ln + lnx + (-1ln + -1lnx) = ln(x + -2)

Reorder the terms:
5ln + -1ln + lnx + -1lnx = ln(x + -2)

Combine like terms: 5ln + -1ln = 4ln
4ln + lnx + -1lnx = ln(x + -2)

Combine like terms: lnx + -1lnx = 0
4ln + 0 = ln(x + -2)
4ln = ln(x + -2)

Reorder the terms:
4ln = ln(-2 + x)
4ln = (-2 * ln + x * ln)
4ln = (-2ln + lnx)

Solving
4ln = -2ln + lnx

Solving for variable 'l'.

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

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

Combine like terms: 4ln + 2ln = 6ln
6ln = -2ln + 2ln + lnx

Combine like terms: -2ln + 2ln = 0
6ln = 0 + lnx
6ln = lnx

Add '-1lnx' to each side of the equation.
6ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
6ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + 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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