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Simplifying ln(-3x + 2) = ln(14) Reorder the terms: ln(2 + -3x) = ln(14) (2 * ln + -3x * ln) = ln(14) (2ln + -3lnx) = ln(14) Reorder the terms for easier multiplication: 2ln + -3lnx = 14ln Solving 2ln + -3lnx = 14ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. 2ln + -14ln + -3lnx = 14ln + -14ln Combine like terms: 2ln + -14ln = -12ln -12ln + -3lnx = 14ln + -14ln Combine like terms: 14ln + -14ln = 0 -12ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-3ln'. -3ln(4 + 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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