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Simplifying lnx + ln(x + -4) = ln(3x + -12) Reorder the terms: lnx + ln(-4 + x) = ln(3x + -12) lnx + (-4 * ln + x * ln) = ln(3x + -12) lnx + (-4ln + lnx) = ln(3x + -12) Reorder the terms: -4ln + lnx + lnx = ln(3x + -12) Combine like terms: lnx + lnx = 2lnx -4ln + 2lnx = ln(3x + -12) Reorder the terms: -4ln + 2lnx = ln(-12 + 3x) -4ln + 2lnx = (-12 * ln + 3x * ln) -4ln + 2lnx = (-12ln + 3lnx) Solving -4ln + 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. -4ln + 12ln + 2lnx = -12ln + 12ln + 3lnx Combine like terms: -4ln + 12ln = 8ln 8ln + 2lnx = -12ln + 12ln + 3lnx Combine like terms: -12ln + 12ln = 0 8ln + 2lnx = 0 + 3lnx 8ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. 8ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx 8ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 8ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(8 + -1x) = 0Subproblem 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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + x 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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