lnx+ln(x+2)=ln(x-12)

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Solution for lnx+ln(x+2)=ln(x-12) equation:


Simplifying
lnx + ln(x + 2) = ln(x + -12)

Reorder the terms:
lnx + ln(2 + x) = ln(x + -12)
lnx + (2 * ln + x * ln) = ln(x + -12)
lnx + (2ln + lnx) = ln(x + -12)

Reorder the terms:
2ln + lnx + lnx = ln(x + -12)

Combine like terms: lnx + lnx = 2lnx
2ln + 2lnx = ln(x + -12)

Reorder the terms:
2ln + 2lnx = ln(-12 + x)
2ln + 2lnx = (-12 * ln + x * ln)
2ln + 2lnx = (-12ln + lnx)

Solving
2ln + 2lnx = -12ln + lnx

Solving for variable 'l'.

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

Add '12ln' to each side of the equation.
2ln + 12ln + 2lnx = -12ln + 12ln + lnx

Combine like terms: 2ln + 12ln = 14ln
14ln + 2lnx = -12ln + 12ln + lnx

Combine like terms: -12ln + 12ln = 0
14ln + 2lnx = 0 + lnx
14ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
14ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
14ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
14ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(14 + 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 '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Add '-1x' to each side of the equation. x + -1x = -14 + -1x Combine like terms: x + -1x = 0 0 = -14 + -1x Simplifying 0 = -14 + -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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