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Simplifying ln(2x + -3) = ln(9) + -1ln(x + -3) Reorder the terms: ln(-3 + 2x) = ln(9) + -1ln(x + -3) (-3 * ln + 2x * ln) = ln(9) + -1ln(x + -3) (-3ln + 2lnx) = ln(9) + -1ln(x + -3) Reorder the terms for easier multiplication: -3ln + 2lnx = 9ln + -1ln(x + -3) Reorder the terms: -3ln + 2lnx = 9ln + -1ln(-3 + x) -3ln + 2lnx = 9ln + (-3 * -1ln + x * -1ln) -3ln + 2lnx = 9ln + (3ln + -1lnx) Combine like terms: 9ln + 3ln = 12ln -3ln + 2lnx = 12ln + -1lnx Solving -3ln + 2lnx = 12ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. -3ln + -12ln + 2lnx = 12ln + -12ln + -1lnx Combine like terms: -3ln + -12ln = -15ln -15ln + 2lnx = 12ln + -12ln + -1lnx Combine like terms: 12ln + -12ln = 0 -15ln + 2lnx = 0 + -1lnx -15ln + 2lnx = -1lnx Add 'lnx' to each side of the equation. -15ln + 2lnx + lnx = -1lnx + lnx Combine like terms: 2lnx + lnx = 3lnx -15ln + 3lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -15ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-5 + x) = 0 Ignore the factor 3.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 '(-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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