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