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Simplifying ln(7 + -1x) + ln(1 + -1x) = ln(25 + -1x) (7 * ln + -1x * ln) + ln(1 + -1x) = ln(25 + -1x) (7ln + -1lnx) + ln(1 + -1x) = ln(25 + -1x) 7ln + -1lnx + (1 * ln + -1x * ln) = ln(25 + -1x) 7ln + -1lnx + (1ln + -1lnx) = ln(25 + -1x) Reorder the terms: 7ln + 1ln + -1lnx + -1lnx = ln(25 + -1x) Combine like terms: 7ln + 1ln = 8ln 8ln + -1lnx + -1lnx = ln(25 + -1x) Combine like terms: -1lnx + -1lnx = -2lnx 8ln + -2lnx = ln(25 + -1x) 8ln + -2lnx = (25 * ln + -1x * ln) 8ln + -2lnx = (25ln + -1lnx) Solving 8ln + -2lnx = 25ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-25ln' to each side of the equation. 8ln + -25ln + -2lnx = 25ln + -25ln + -1lnx Combine like terms: 8ln + -25ln = -17ln -17ln + -2lnx = 25ln + -25ln + -1lnx Combine like terms: 25ln + -25ln = 0 -17ln + -2lnx = 0 + -1lnx -17ln + -2lnx = -1lnx Add 'lnx' to each side of the equation. -17ln + -2lnx + lnx = -1lnx + lnx Combine like terms: -2lnx + lnx = -1lnx -17ln + -1lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -17ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(17 + x) = 0 Ignore the factor -1.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 '(17 + x)' equal to zero and attempt to solve: Simplifying 17 + x = 0 Solving 17 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + x = 0 + -17 x = 0 + -17 Combine like terms: 0 + -17 = -17 x = -17 Add '-1x' to each side of the equation. x + -1x = -17 + -1x Combine like terms: x + -1x = 0 0 = -17 + -1x Simplifying 0 = -17 + -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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