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Simplifying ln(x + 1) + ln(2x + -4) = 2ln * 6 Reorder the terms: ln(1 + x) + ln(2x + -4) = 2ln * 6 (1 * ln + x * ln) + ln(2x + -4) = 2ln * 6 (1ln + lnx) + ln(2x + -4) = 2ln * 6 Reorder the terms: 1ln + lnx + ln(-4 + 2x) = 2ln * 6 1ln + lnx + (-4 * ln + 2x * ln) = 2ln * 6 1ln + lnx + (-4ln + 2lnx) = 2ln * 6 Reorder the terms: 1ln + -4ln + lnx + 2lnx = 2ln * 6 Combine like terms: 1ln + -4ln = -3ln -3ln + lnx + 2lnx = 2ln * 6 Combine like terms: lnx + 2lnx = 3lnx -3ln + 3lnx = 2ln * 6 Reorder the terms for easier multiplication: -3ln + 3lnx = 2 * 6ln Multiply 2 * 6 -3ln + 3lnx = 12ln Solving -3ln + 3lnx = 12ln 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. -3ln + -12ln + 3lnx = 12ln + -12ln Combine like terms: -3ln + -12ln = -15ln -15ln + 3lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -15ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-5 + x) = 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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -1x 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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