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Simplifying ln(7x + 12) + -1ln(x + 3) = lnx Reorder the terms: ln(12 + 7x) + -1ln(x + 3) = lnx (12 * ln + 7x * ln) + -1ln(x + 3) = lnx (12ln + 7lnx) + -1ln(x + 3) = lnx Reorder the terms: 12ln + 7lnx + -1ln(3 + x) = lnx 12ln + 7lnx + (3 * -1ln + x * -1ln) = lnx 12ln + 7lnx + (-3ln + -1lnx) = lnx Reorder the terms: 12ln + -3ln + 7lnx + -1lnx = lnx Combine like terms: 12ln + -3ln = 9ln 9ln + 7lnx + -1lnx = lnx Combine like terms: 7lnx + -1lnx = 6lnx 9ln + 6lnx = lnx Solving 9ln + 6lnx = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. 9ln + 6lnx + -1lnx = lnx + -1lnx Combine like terms: 6lnx + -1lnx = 5lnx 9ln + 5lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 9ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + 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 '(9 + 5x)' equal to zero and attempt to solve: Simplifying 9 + 5x = 0 Solving 9 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5x = 0 + -9 5x = 0 + -9 Combine like terms: 0 + -9 = -9 5x = -9 Add '-5x' to each side of the equation. 5x + -5x = -9 + -5x Combine like terms: 5x + -5x = 0 0 = -9 + -5x Simplifying 0 = -9 + -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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