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Simplifying ln(2x + -7) = ln(5x + -16) Reorder the terms: ln(-7 + 2x) = ln(5x + -16) (-7 * ln + 2x * ln) = ln(5x + -16) (-7ln + 2lnx) = ln(5x + -16) Reorder the terms: -7ln + 2lnx = ln(-16 + 5x) -7ln + 2lnx = (-16 * ln + 5x * ln) -7ln + 2lnx = (-16ln + 5lnx) Solving -7ln + 2lnx = -16ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '16ln' to each side of the equation. -7ln + 16ln + 2lnx = -16ln + 16ln + 5lnx Combine like terms: -7ln + 16ln = 9ln 9ln + 2lnx = -16ln + 16ln + 5lnx Combine like terms: -16ln + 16ln = 0 9ln + 2lnx = 0 + 5lnx 9ln + 2lnx = 5lnx Add '-5lnx' to each side of the equation. 9ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx 9ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 9ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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