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