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

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


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

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

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

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

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

Combine like terms: lnx + -1lnx = 0
-2ln + 0 = ln(x + 5)
-2ln = ln(x + 5)

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

Solving
-2ln = 5ln + lnx

Solving for variable 'l'.

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

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

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

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

Add '-1lnx' to each side of the equation.
-7ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-7ln + -1lnx = 0

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

Ignore the factor -1.

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 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -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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