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Simplifying ln(x + 2) + ln(x + -2) = ln[6(x + 2)] Reorder the terms: ln(2 + x) + ln(x + -2) = ln[6(x + 2)] (2 * ln + x * ln) + ln(x + -2) = ln[6(x + 2)] (2ln + lnx) + ln(x + -2) = ln[6(x + 2)] Reorder the terms: 2ln + lnx + ln(-2 + x) = ln[6(x + 2)] 2ln + lnx + (-2 * ln + x * ln) = ln[6(x + 2)] 2ln + lnx + (-2ln + lnx) = ln[6(x + 2)] Reorder the terms: 2ln + -2ln + lnx + lnx = ln[6(x + 2)] Combine like terms: 2ln + -2ln = 0 0 + lnx + lnx = ln[6(x + 2)] lnx + lnx = ln[6(x + 2)] Combine like terms: lnx + lnx = 2lnx 2lnx = ln[6(x + 2)] Reorder the terms: 2lnx = ln[6(2 + x)] 2lnx = ln[(2 * 6 + x * 6)] 2lnx = ln[(12 + 6x)] 2lnx = [12 * ln + 6x * ln] 2lnx = [12ln + 6lnx] Solving 2lnx = 12ln + 6lnx 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. -12ln + 2lnx = 12ln + -12ln + 6lnx Combine like terms: 12ln + -12ln = 0 -12ln + 2lnx = 0 + 6lnx -12ln + 2lnx = 6lnx Add '-6lnx' to each side of the equation. -12ln + 2lnx + -6lnx = 6lnx + -6lnx Combine like terms: 2lnx + -6lnx = -4lnx -12ln + -4lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -12ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '-4ln'. -4ln(3 + x) = 0 Ignore the factor -4.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 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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