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Simplifying ln(1 + -1x) + ln(3 + -1x) = ln(8) (1 * ln + -1x * ln) + ln(3 + -1x) = ln(8) (1ln + -1lnx) + ln(3 + -1x) = ln(8) 1ln + -1lnx + (3 * ln + -1x * ln) = ln(8) 1ln + -1lnx + (3ln + -1lnx) = ln(8) Reorder the terms: 1ln + 3ln + -1lnx + -1lnx = ln(8) Combine like terms: 1ln + 3ln = 4ln 4ln + -1lnx + -1lnx = ln(8) Combine like terms: -1lnx + -1lnx = -2lnx 4ln + -2lnx = ln(8) Reorder the terms for easier multiplication: 4ln + -2lnx = 8ln Solving 4ln + -2lnx = 8ln 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. 4ln + -8ln + -2lnx = 8ln + -8ln Combine like terms: 4ln + -8ln = -4ln -4ln + -2lnx = 8ln + -8ln Combine like terms: 8ln + -8ln = 0 -4ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(2 + 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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