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Simplifying ln(x + -2) = 2ln(x) + -1ln(2x + -3) Reorder the terms: ln(-2 + x) = 2ln(x) + -1ln(2x + -3) (-2 * ln + x * ln) = 2ln(x) + -1ln(2x + -3) (-2ln + lnx) = 2ln(x) + -1ln(2x + -3) Multiply ln * x -2ln + lnx = 2lnx + -1ln(2x + -3) Reorder the terms: -2ln + lnx = 2lnx + -1ln(-3 + 2x) -2ln + lnx = 2lnx + (-3 * -1ln + 2x * -1ln) -2ln + lnx = 2lnx + (3ln + -2lnx) Reorder the terms: -2ln + lnx = 3ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -2ln + lnx = 3ln + 0 -2ln + lnx = 3ln Solving -2ln + lnx = 3ln 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. -2ln + -3ln + lnx = 3ln + -3ln Combine like terms: -2ln + -3ln = -5ln -5ln + lnx = 3ln + -3ln Combine like terms: 3ln + -3ln = 0 -5ln + lnx = 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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