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Simplifying 2ln(x + -1) = ln(x + 5) Reorder the terms: 2ln(-1 + x) = ln(x + 5) (-1 * 2ln + x * 2ln) = ln(x + 5) (-2ln + 2lnx) = ln(x + 5) Reorder the terms: -2ln + 2lnx = ln(5 + x) -2ln + 2lnx = (5 * ln + x * ln) -2ln + 2lnx = (5ln + lnx) Solving -2ln + 2lnx = 5ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. -2ln + -5ln + 2lnx = 5ln + -5ln + lnx Combine like terms: -2ln + -5ln = -7ln -7ln + 2lnx = 5ln + -5ln + lnx Combine like terms: 5ln + -5ln = 0 -7ln + 2lnx = 0 + lnx -7ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -7ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -7ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -7ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + 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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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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