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Simplifying ln(7 + -1x) = 1ln(x + -1) (7 * ln + -1x * ln) = 1ln(x + -1) (7ln + -1lnx) = 1ln(x + -1) Reorder the terms: 7ln + -1lnx = 1ln(-1 + x) 7ln + -1lnx = (-1 * 1ln + x * 1ln) 7ln + -1lnx = (-1ln + 1lnx) Solving 7ln + -1lnx = -1ln + 1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. 7ln + ln + -1lnx = -1ln + ln + 1lnx Combine like terms: 7ln + ln = 8ln 8ln + -1lnx = -1ln + ln + 1lnx Combine like terms: -1ln + ln = 0 8ln + -1lnx = 0 + 1lnx 8ln + -1lnx = 1lnx Add '-1lnx' to each side of the equation. 8ln + -1lnx + -1lnx = 1lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx 8ln + -2lnx = 1lnx + -1lnx Combine like terms: 1lnx + -1lnx = 0 8ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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