ln(x-8)=ln(x+4)-ln(x-6)

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Solution for ln(x-8)=ln(x+4)-ln(x-6) equation:


Simplifying
ln(x + -8) = ln(x + 4) + -1ln(x + -6)

Reorder the terms:
ln(-8 + x) = ln(x + 4) + -1ln(x + -6)
(-8 * ln + x * ln) = ln(x + 4) + -1ln(x + -6)
(-8ln + lnx) = ln(x + 4) + -1ln(x + -6)

Reorder the terms:
-8ln + lnx = ln(4 + x) + -1ln(x + -6)
-8ln + lnx = (4 * ln + x * ln) + -1ln(x + -6)
-8ln + lnx = (4ln + lnx) + -1ln(x + -6)

Reorder the terms:
-8ln + lnx = 4ln + lnx + -1ln(-6 + x)
-8ln + lnx = 4ln + lnx + (-6 * -1ln + x * -1ln)
-8ln + lnx = 4ln + lnx + (6ln + -1lnx)

Reorder the terms:
-8ln + lnx = 4ln + 6ln + lnx + -1lnx

Combine like terms: 4ln + 6ln = 10ln
-8ln + lnx = 10ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-8ln + lnx = 10ln + 0
-8ln + lnx = 10ln

Solving
-8ln + lnx = 10ln

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
-8ln + -10ln + lnx = 10ln + -10ln

Combine like terms: -8ln + -10ln = -18ln
-18ln + lnx = 10ln + -10ln

Combine like terms: 10ln + -10ln = 0
-18ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-18 + x) = 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 '(-18 + x)' equal to zero and attempt to solve: Simplifying -18 + x = 0 Solving -18 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 0 + 18 Combine like terms: -18 + 18 = 0 0 + x = 0 + 18 x = 0 + 18 Combine like terms: 0 + 18 = 18 x = 18 Add '-1x' to each side of the equation. x + -1x = 18 + -1x Combine like terms: x + -1x = 0 0 = 18 + -1x Simplifying 0 = 18 + -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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