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Simplifying ln(x + -2) + ln(x + -3) = ln(3x + 2) Reorder the terms: ln(-2 + x) + ln(x + -3) = ln(3x + 2) (-2 * ln + x * ln) + ln(x + -3) = ln(3x + 2) (-2ln + lnx) + ln(x + -3) = ln(3x + 2) Reorder the terms: -2ln + lnx + ln(-3 + x) = ln(3x + 2) -2ln + lnx + (-3 * ln + x * ln) = ln(3x + 2) -2ln + lnx + (-3ln + lnx) = ln(3x + 2) Reorder the terms: -2ln + -3ln + lnx + lnx = ln(3x + 2) Combine like terms: -2ln + -3ln = -5ln -5ln + lnx + lnx = ln(3x + 2) Combine like terms: lnx + lnx = 2lnx -5ln + 2lnx = ln(3x + 2) Reorder the terms: -5ln + 2lnx = ln(2 + 3x) -5ln + 2lnx = (2 * ln + 3x * ln) -5ln + 2lnx = (2ln + 3lnx) Solving -5ln + 2lnx = 2ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. -5ln + -2ln + 2lnx = 2ln + -2ln + 3lnx Combine like terms: -5ln + -2ln = -7ln -7ln + 2lnx = 2ln + -2ln + 3lnx Combine like terms: 2ln + -2ln = 0 -7ln + 2lnx = 0 + 3lnx -7ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. -7ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx -7ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -7ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(7 + 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -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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