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Simplifying 2ln(x + -1) = ln(-1x + 43) Reorder the terms: 2ln(-1 + x) = ln(-1x + 43) (-1 * 2ln + x * 2ln) = ln(-1x + 43) (-2ln + 2lnx) = ln(-1x + 43) Reorder the terms: -2ln + 2lnx = ln(43 + -1x) -2ln + 2lnx = (43 * ln + -1x * ln) -2ln + 2lnx = (43ln + -1lnx) Solving -2ln + 2lnx = 43ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-43ln' to each side of the equation. -2ln + -43ln + 2lnx = 43ln + -43ln + -1lnx Combine like terms: -2ln + -43ln = -45ln -45ln + 2lnx = 43ln + -43ln + -1lnx Combine like terms: 43ln + -43ln = 0 -45ln + 2lnx = 0 + -1lnx -45ln + 2lnx = -1lnx Add 'lnx' to each side of the equation. -45ln + 2lnx + lnx = -1lnx + lnx Combine like terms: 2lnx + lnx = 3lnx -45ln + 3lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -45ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-15 + x) = 0 Ignore the factor 3.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 '(-15 + x)' equal to zero and attempt to solve: Simplifying -15 + x = 0 Solving -15 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + x = 0 + 15 x = 0 + 15 Combine like terms: 0 + 15 = 15 x = 15 Add '-1x' to each side of the equation. x + -1x = 15 + -1x Combine like terms: x + -1x = 0 0 = 15 + -1x Simplifying 0 = 15 + -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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