ln(x-1)+ln(x-2)=ln(x+14)

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Solution for ln(x-1)+ln(x-2)=ln(x+14) equation:


Simplifying
ln(x + -1) + ln(x + -2) = ln(x + 14)

Reorder the terms:
ln(-1 + x) + ln(x + -2) = ln(x + 14)
(-1 * ln + x * ln) + ln(x + -2) = ln(x + 14)
(-1ln + lnx) + ln(x + -2) = ln(x + 14)

Reorder the terms:
-1ln + lnx + ln(-2 + x) = ln(x + 14)
-1ln + lnx + (-2 * ln + x * ln) = ln(x + 14)
-1ln + lnx + (-2ln + lnx) = ln(x + 14)

Reorder the terms:
-1ln + -2ln + lnx + lnx = ln(x + 14)

Combine like terms: -1ln + -2ln = -3ln
-3ln + lnx + lnx = ln(x + 14)

Combine like terms: lnx + lnx = 2lnx
-3ln + 2lnx = ln(x + 14)

Reorder the terms:
-3ln + 2lnx = ln(14 + x)
-3ln + 2lnx = (14 * ln + x * ln)
-3ln + 2lnx = (14ln + lnx)

Solving
-3ln + 2lnx = 14ln + lnx

Solving for variable 'l'.

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

Add '-14ln' to each side of the equation.
-3ln + -14ln + 2lnx = 14ln + -14ln + lnx

Combine like terms: -3ln + -14ln = -17ln
-17ln + 2lnx = 14ln + -14ln + lnx

Combine like terms: 14ln + -14ln = 0
-17ln + 2lnx = 0 + lnx
-17ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-17ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-17ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-17ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-17 + 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 '(-17 + x)' equal to zero and attempt to solve: Simplifying -17 + x = 0 Solving -17 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + x = 0 + 17 x = 0 + 17 Combine like terms: 0 + 17 = 17 x = 17 Add '-1x' to each side of the equation. x + -1x = 17 + -1x Combine like terms: x + -1x = 0 0 = 17 + -1x Simplifying 0 = 17 + -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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