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Simplifying ln(2x + -9) = ln(-5x + 19) Reorder the terms: ln(-9 + 2x) = ln(-5x + 19) (-9 * ln + 2x * ln) = ln(-5x + 19) (-9ln + 2lnx) = ln(-5x + 19) Reorder the terms: -9ln + 2lnx = ln(19 + -5x) -9ln + 2lnx = (19 * ln + -5x * ln) -9ln + 2lnx = (19ln + -5lnx) Solving -9ln + 2lnx = 19ln + -5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-19ln' to each side of the equation. -9ln + -19ln + 2lnx = 19ln + -19ln + -5lnx Combine like terms: -9ln + -19ln = -28ln -28ln + 2lnx = 19ln + -19ln + -5lnx Combine like terms: 19ln + -19ln = 0 -28ln + 2lnx = 0 + -5lnx -28ln + 2lnx = -5lnx Add '5lnx' to each side of the equation. -28ln + 2lnx + 5lnx = -5lnx + 5lnx Combine like terms: 2lnx + 5lnx = 7lnx -28ln + 7lnx = -5lnx + 5lnx Combine like terms: -5lnx + 5lnx = 0 -28ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), '7ln'. 7ln(-4 + x) = 0 Ignore the factor 7.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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