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Simplifying 2ln(x + 1) = ln(8 + -4x) Reorder the terms: 2ln(1 + x) = ln(8 + -4x) (1 * 2ln + x * 2ln) = ln(8 + -4x) (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 = -6ln -6ln + 2lnx = 8ln + -8ln + -4lnx Combine like terms: 8ln + -8ln = 0 -6ln + 2lnx = 0 + -4lnx -6ln + 2lnx = -4lnx Add '4lnx' to each side of the equation. -6ln + 2lnx + 4lnx = -4lnx + 4lnx Combine like terms: 2lnx + 4lnx = 6lnx -6ln + 6lnx = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 -6ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(-1 + x) = 0 Ignore the factor 6.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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