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Simplifying ln(x + -3) + ln(x + -2) = ln(4x + -12) Reorder the terms: ln(-3 + x) + ln(x + -2) = ln(4x + -12) (-3 * ln + x * ln) + ln(x + -2) = ln(4x + -12) (-3ln + lnx) + ln(x + -2) = ln(4x + -12) Reorder the terms: -3ln + lnx + ln(-2 + x) = ln(4x + -12) -3ln + lnx + (-2 * ln + x * ln) = ln(4x + -12) -3ln + lnx + (-2ln + lnx) = ln(4x + -12) Reorder the terms: -3ln + -2ln + lnx + lnx = ln(4x + -12) Combine like terms: -3ln + -2ln = -5ln -5ln + lnx + lnx = ln(4x + -12) Combine like terms: lnx + lnx = 2lnx -5ln + 2lnx = ln(4x + -12) Reorder the terms: -5ln + 2lnx = ln(-12 + 4x) -5ln + 2lnx = (-12 * ln + 4x * ln) -5ln + 2lnx = (-12ln + 4lnx) Solving -5ln + 2lnx = -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. -5ln + 12ln + 2lnx = -12ln + 12ln + 4lnx Combine like terms: -5ln + 12ln = 7ln 7ln + 2lnx = -12ln + 12ln + 4lnx Combine like terms: -12ln + 12ln = 0 7ln + 2lnx = 0 + 4lnx 7ln + 2lnx = 4lnx Add '-4lnx' to each side of the equation. 7ln + 2lnx + -4lnx = 4lnx + -4lnx Combine like terms: 2lnx + -4lnx = -2lnx 7ln + -2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 7ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + -2x) = 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 '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Add '2x' to each side of the equation. -2x + 2x = -7 + 2x Combine like terms: -2x + 2x = 0 0 = -7 + 2x Simplifying 0 = -7 + 2x 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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