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Simplifying 2lnx = ln(5x + -6) Reorder the terms: 2lnx = ln(-6 + 5x) 2lnx = (-6 * ln + 5x * ln) 2lnx = (-6ln + 5lnx) Solving 2lnx = -6ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. 6ln + 2lnx = -6ln + 6ln + 5lnx Combine like terms: -6ln + 6ln = 0 6ln + 2lnx = 0 + 5lnx 6ln + 2lnx = 5lnx Add '-5lnx' to each side of the equation. 6ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx 6ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 6ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(2 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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