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Simplifying ln(2x + 3) = ln(5x + 7) Reorder the terms: ln(3 + 2x) = ln(5x + 7) (3 * ln + 2x * ln) = ln(5x + 7) (3ln + 2lnx) = ln(5x + 7) Reorder the terms: 3ln + 2lnx = ln(7 + 5x) 3ln + 2lnx = (7 * ln + 5x * ln) 3ln + 2lnx = (7ln + 5lnx) Solving 3ln + 2lnx = 7ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. 3ln + -7ln + 2lnx = 7ln + -7ln + 5lnx Combine like terms: 3ln + -7ln = -4ln -4ln + 2lnx = 7ln + -7ln + 5lnx Combine like terms: 7ln + -7ln = 0 -4ln + 2lnx = 0 + 5lnx -4ln + 2lnx = 5lnx Add '-5lnx' to each side of the equation. -4ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx -4ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -4ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(4 + 3x) = 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 '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 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 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Add '-3x' to each side of the equation. 3x + -3x = -4 + -3x Combine like terms: 3x + -3x = 0 0 = -4 + -3x Simplifying 0 = -4 + -3x 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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