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Simplifying ln(x + 2) + 7ln(x + -2) + 6ln(x) = 0 Reorder the terms: ln(2 + x) + 7ln(x + -2) + 6ln(x) = 0 (2 * ln + x * ln) + 7ln(x + -2) + 6ln(x) = 0 (2ln + lnx) + 7ln(x + -2) + 6ln(x) = 0 Reorder the terms: 2ln + lnx + 7ln(-2 + x) + 6ln(x) = 0 2ln + lnx + (-2 * 7ln + x * 7ln) + 6ln(x) = 0 2ln + lnx + (-14ln + 7lnx) + 6ln(x) = 0 Multiply ln * x 2ln + lnx + -14ln + 7lnx + 6lnx = 0 Reorder the terms: 2ln + -14ln + lnx + 7lnx + 6lnx = 0 Combine like terms: 2ln + -14ln = -12ln -12ln + lnx + 7lnx + 6lnx = 0 Combine like terms: lnx + 7lnx = 8lnx -12ln + 8lnx + 6lnx = 0 Combine like terms: 8lnx + 6lnx = 14lnx -12ln + 14lnx = 0 Solving -12ln + 14lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-6 + 7x) = 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 '(-6 + 7x)' equal to zero and attempt to solve: Simplifying -6 + 7x = 0 Solving -6 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 7x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 7x = 0 + 6 7x = 0 + 6 Combine like terms: 0 + 6 = 6 7x = 6 Add '-7x' to each side of the equation. 7x + -7x = 6 + -7x Combine like terms: 7x + -7x = 0 0 = 6 + -7x Simplifying 0 = 6 + -7x 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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