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