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Simplifying ln(x + 7) + lnx = ln(5x + 3) Reorder the terms: ln(7 + x) + lnx = ln(5x + 3) (7 * ln + x * ln) + lnx = ln(5x + 3) (7ln + lnx) + lnx = ln(5x + 3) Combine like terms: lnx + lnx = 2lnx 7ln + 2lnx = ln(5x + 3) Reorder the terms: 7ln + 2lnx = ln(3 + 5x) 7ln + 2lnx = (3 * ln + 5x * ln) 7ln + 2lnx = (3ln + 5lnx) Solving 7ln + 2lnx = 3ln + 5lnx 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 + 5lnx Combine like terms: 7ln + -3ln = 4ln 4ln + 2lnx = 3ln + -3ln + 5lnx Combine like terms: 3ln + -3ln = 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), 'ln'. ln(4 + -3x) = 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 + -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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