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