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Simplifying ln(3x + 7) = ln(6x + -2) Reorder the terms: ln(7 + 3x) = ln(6x + -2) (7 * ln + 3x * ln) = ln(6x + -2) (7ln + 3lnx) = ln(6x + -2) Reorder the terms: 7ln + 3lnx = ln(-2 + 6x) 7ln + 3lnx = (-2 * ln + 6x * ln) 7ln + 3lnx = (-2ln + 6lnx) Solving 7ln + 3lnx = -2ln + 6lnx 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. 7ln + 2ln + 3lnx = -2ln + 2ln + 6lnx Combine like terms: 7ln + 2ln = 9ln 9ln + 3lnx = -2ln + 2ln + 6lnx Combine like terms: -2ln + 2ln = 0 9ln + 3lnx = 0 + 6lnx 9ln + 3lnx = 6lnx Add '-6lnx' to each side of the equation. 9ln + 3lnx + -6lnx = 6lnx + -6lnx Combine like terms: 3lnx + -6lnx = -3lnx 9ln + -3lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 9ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(3 + -1x) = 0 Ignore the factor 3.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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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