ln(x)+ln(x-1)=ln(3x+12)

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Solution for ln(x)+ln(x-1)=ln(3x+12) equation:


Simplifying
ln(x) + ln(x + -1) = ln(3x + 12)

Multiply ln * x
lnx + ln(x + -1) = ln(3x + 12)

Reorder the terms:
lnx + ln(-1 + x) = ln(3x + 12)
lnx + (-1 * ln + x * ln) = ln(3x + 12)
lnx + (-1ln + lnx) = ln(3x + 12)

Reorder the terms:
-1ln + lnx + lnx = ln(3x + 12)

Combine like terms: lnx + lnx = 2lnx
-1ln + 2lnx = ln(3x + 12)

Reorder the terms:
-1ln + 2lnx = ln(12 + 3x)
-1ln + 2lnx = (12 * ln + 3x * ln)
-1ln + 2lnx = (12ln + 3lnx)

Solving
-1ln + 2lnx = 12ln + 3lnx

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.
-1ln + -12ln + 2lnx = 12ln + -12ln + 3lnx

Combine like terms: -1ln + -12ln = -13ln
-13ln + 2lnx = 12ln + -12ln + 3lnx

Combine like terms: 12ln + -12ln = 0
-13ln + 2lnx = 0 + 3lnx
-13ln + 2lnx = 3lnx

Add '-3lnx' to each side of the equation.
-13ln + 2lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 2lnx + -3lnx = -1lnx
-13ln + -1lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-13ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(13 + 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 '(13 + x)' equal to zero and attempt to solve: Simplifying 13 + x = 0 Solving 13 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + x = 0 + -13 x = 0 + -13 Combine like terms: 0 + -13 = -13 x = -13 Add '-1x' to each side of the equation. x + -1x = -13 + -1x Combine like terms: x + -1x = 0 0 = -13 + -1x Simplifying 0 = -13 + -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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