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