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Simplifying 2lnx + ln(2x + -1) = ln(5x + 2) Reorder the terms: 2lnx + ln(-1 + 2x) = ln(5x + 2) 2lnx + (-1 * ln + 2x * ln) = ln(5x + 2) 2lnx + (-1ln + 2lnx) = ln(5x + 2) Reorder the terms: -1ln + 2lnx + 2lnx = ln(5x + 2) Combine like terms: 2lnx + 2lnx = 4lnx -1ln + 4lnx = ln(5x + 2) Reorder the terms: -1ln + 4lnx = ln(2 + 5x) -1ln + 4lnx = (2 * ln + 5x * ln) -1ln + 4lnx = (2ln + 5lnx) Solving -1ln + 4lnx = 2ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. -1ln + -2ln + 4lnx = 2ln + -2ln + 5lnx Combine like terms: -1ln + -2ln = -3ln -3ln + 4lnx = 2ln + -2ln + 5lnx Combine like terms: 2ln + -2ln = 0 -3ln + 4lnx = 0 + 5lnx -3ln + 4lnx = 5lnx Add '-5lnx' to each side of the equation. -3ln + 4lnx + -5lnx = 5lnx + -5lnx Combine like terms: 4lnx + -5lnx = -1lnx -3ln + -1lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -3ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(3 + x) = 0 Ignore the factor -1.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 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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