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Simplifying 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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