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Simplifying ln(7x + 12) + -1ln(x) = ln(8) Reorder the terms: ln(12 + 7x) + -1ln(x) = ln(8) (12 * ln + 7x * ln) + -1ln(x) = ln(8) (12ln + 7lnx) + -1ln(x) = ln(8) Multiply ln * x 12ln + 7lnx + -1lnx = ln(8) Combine like terms: 7lnx + -1lnx = 6lnx 12ln + 6lnx = ln(8) Reorder the terms for easier multiplication: 12ln + 6lnx = 8ln Solving 12ln + 6lnx = 8ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 12ln + -8ln + 6lnx = 8ln + -8ln Combine like terms: 12ln + -8ln = 4ln 4ln + 6lnx = 8ln + -8ln Combine like terms: 8ln + -8ln = 0 4ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(2 + 3x) = 0 Ignore the factor 2.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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Add '-3x' to each side of the equation. 3x + -3x = -2 + -3x Combine like terms: 3x + -3x = 0 0 = -2 + -3x Simplifying 0 = -2 + -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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