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Simplifying ln(x + 3) = ln(2x + -3) Reorder the terms: ln(3 + x) = ln(2x + -3) (3 * ln + x * ln) = ln(2x + -3) (3ln + lnx) = ln(2x + -3) Reorder the terms: 3ln + lnx = ln(-3 + 2x) 3ln + lnx = (-3 * ln + 2x * ln) 3ln + lnx = (-3ln + 2lnx) Solving 3ln + lnx = -3ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '3ln' to each side of the equation. 3ln + 3ln + lnx = -3ln + 3ln + 2lnx Combine like terms: 3ln + 3ln = 6ln 6ln + lnx = -3ln + 3ln + 2lnx Combine like terms: -3ln + 3ln = 0 6ln + lnx = 0 + 2lnx 6ln + lnx = 2lnx Add '-2lnx' to each side of the equation. 6ln + lnx + -2lnx = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx 6ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 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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