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Simplifying 2ln(x + -1) = ln(4x + 8) Reorder the terms: 2ln(-1 + x) = ln(4x + 8) (-1 * 2ln + x * 2ln) = ln(4x + 8) (-2ln + 2lnx) = ln(4x + 8) Reorder the terms: -2ln + 2lnx = ln(8 + 4x) -2ln + 2lnx = (8 * ln + 4x * ln) -2ln + 2lnx = (8ln + 4lnx) Solving -2ln + 2lnx = 8ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. -2ln + -8ln + 2lnx = 8ln + -8ln + 4lnx Combine like terms: -2ln + -8ln = -10ln -10ln + 2lnx = 8ln + -8ln + 4lnx Combine like terms: 8ln + -8ln = 0 -10ln + 2lnx = 0 + 4lnx -10ln + 2lnx = 4lnx Add '-4lnx' to each side of the equation. -10ln + 2lnx + -4lnx = 4lnx + -4lnx Combine like terms: 2lnx + -4lnx = -2lnx -10ln + -2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -10ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(5 + x) = 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 '(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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