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Simplifying ln(2x + -3) = 2lnx + -1ln(x + -2) Reorder the terms: ln(-3 + 2x) = 2lnx + -1ln(x + -2) (-3 * ln + 2x * ln) = 2lnx + -1ln(x + -2) (-3ln + 2lnx) = 2lnx + -1ln(x + -2) Reorder the terms: -3ln + 2lnx = 2lnx + -1ln(-2 + x) -3ln + 2lnx = 2lnx + (-2 * -1ln + x * -1ln) -3ln + 2lnx = 2lnx + (2ln + -1lnx) Reorder the terms: -3ln + 2lnx = 2ln + 2lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -3ln + 2lnx = 2ln + 1lnx Solving -3ln + 2lnx = 2ln + 1lnx 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 + 1lnx Combine like terms: -3ln + -2ln = -5ln -5ln + 2lnx = 2ln + -2ln + 1lnx Combine like terms: 2ln + -2ln = 0 -5ln + 2lnx = 0 + 1lnx -5ln + 2lnx = 1lnx Add '-1lnx' to each side of the equation. -5ln + 2lnx + -1lnx = 1lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -5ln + 1lnx = 1lnx + -1lnx Combine like terms: 1lnx + -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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