ln(x-6)+ln(x+7)=ln(x-15)

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Solution for ln(x-6)+ln(x+7)=ln(x-15) equation:


Simplifying
ln(x + -6) + ln(x + 7) = ln(x + -15)

Reorder the terms:
ln(-6 + x) + ln(x + 7) = ln(x + -15)
(-6 * ln + x * ln) + ln(x + 7) = ln(x + -15)
(-6ln + lnx) + ln(x + 7) = ln(x + -15)

Reorder the terms:
-6ln + lnx + ln(7 + x) = ln(x + -15)
-6ln + lnx + (7 * ln + x * ln) = ln(x + -15)
-6ln + lnx + (7ln + lnx) = ln(x + -15)

Reorder the terms:
-6ln + 7ln + lnx + lnx = ln(x + -15)

Combine like terms: -6ln + 7ln = 1ln
1ln + lnx + lnx = ln(x + -15)

Combine like terms: lnx + lnx = 2lnx
1ln + 2lnx = ln(x + -15)

Reorder the terms:
1ln + 2lnx = ln(-15 + x)
1ln + 2lnx = (-15 * ln + x * ln)
1ln + 2lnx = (-15ln + lnx)

Solving
1ln + 2lnx = -15ln + lnx

Solving for variable 'l'.

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

Add '15ln' to each side of the equation.
1ln + 15ln + 2lnx = -15ln + 15ln + lnx

Combine like terms: 1ln + 15ln = 16ln
16ln + 2lnx = -15ln + 15ln + lnx

Combine like terms: -15ln + 15ln = 0
16ln + 2lnx = 0 + lnx
16ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
16ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
16ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
16ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(16 + 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 '(16 + x)' equal to zero and attempt to solve: Simplifying 16 + x = 0 Solving 16 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 0 + -16 Combine like terms: 16 + -16 = 0 0 + x = 0 + -16 x = 0 + -16 Combine like terms: 0 + -16 = -16 x = -16 Add '-1x' to each side of the equation. x + -1x = -16 + -1x Combine like terms: x + -1x = 0 0 = -16 + -1x Simplifying 0 = -16 + -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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