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Simplifying lnx + 2ln(x + -3) = ln(4x + -12) Reorder the terms: lnx + 2ln(-3 + x) = ln(4x + -12) lnx + (-3 * 2ln + x * 2ln) = ln(4x + -12) lnx + (-6ln + 2lnx) = ln(4x + -12) Reorder the terms: -6ln + lnx + 2lnx = ln(4x + -12) Combine like terms: lnx + 2lnx = 3lnx -6ln + 3lnx = ln(4x + -12) Reorder the terms: -6ln + 3lnx = ln(-12 + 4x) -6ln + 3lnx = (-12 * ln + 4x * ln) -6ln + 3lnx = (-12ln + 4lnx) Solving -6ln + 3lnx = -12ln + 4lnx 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. -6ln + 12ln + 3lnx = -12ln + 12ln + 4lnx Combine like terms: -6ln + 12ln = 6ln 6ln + 3lnx = -12ln + 12ln + 4lnx Combine like terms: -12ln + 12ln = 0 6ln + 3lnx = 0 + 4lnx 6ln + 3lnx = 4lnx Add '-4lnx' to each side of the equation. 6ln + 3lnx + -4lnx = 4lnx + -4lnx Combine like terms: 3lnx + -4lnx = -1lnx 6ln + -1lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 6ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + 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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