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Simplifying ln(5x + 6) = 2ln(5x + -6) Reorder the terms: ln(6 + 5x) = 2ln(5x + -6) (6 * ln + 5x * ln) = 2ln(5x + -6) (6ln + 5lnx) = 2ln(5x + -6) Reorder the terms: 6ln + 5lnx = 2ln(-6 + 5x) 6ln + 5lnx = (-6 * 2ln + 5x * 2ln) 6ln + 5lnx = (-12ln + 10lnx) Solving 6ln + 5lnx = -12ln + 10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. 6ln + 12ln + 5lnx = -12ln + 12ln + 10lnx Combine like terms: 6ln + 12ln = 18ln 18ln + 5lnx = -12ln + 12ln + 10lnx Combine like terms: -12ln + 12ln = 0 18ln + 5lnx = 0 + 10lnx 18ln + 5lnx = 10lnx Add '-10lnx' to each side of the equation. 18ln + 5lnx + -10lnx = 10lnx + -10lnx Combine like terms: 5lnx + -10lnx = -5lnx 18ln + -5lnx = 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 18ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(18 + -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 '(18 + -5x)' equal to zero and attempt to solve: Simplifying 18 + -5x = 0 Solving 18 + -5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -5x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -5x = 0 + -18 -5x = 0 + -18 Combine like terms: 0 + -18 = -18 -5x = -18 Add '5x' to each side of the equation. -5x + 5x = -18 + 5x Combine like terms: -5x + 5x = 0 0 = -18 + 5x Simplifying 0 = -18 + 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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