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Simplifying ln(2 + -1x) + ln(3) = 2ln(x + -1) (2 * ln + -1x * ln) + ln(3) = 2ln(x + -1) (2ln + -1lnx) + ln(3) = 2ln(x + -1) Reorder the terms for easier multiplication: 2ln + -1lnx + 3ln = 2ln(x + -1) Reorder the terms: 2ln + 3ln + -1lnx = 2ln(x + -1) Combine like terms: 2ln + 3ln = 5ln 5ln + -1lnx = 2ln(x + -1) Reorder the terms: 5ln + -1lnx = 2ln(-1 + x) 5ln + -1lnx = (-1 * 2ln + x * 2ln) 5ln + -1lnx = (-2ln + 2lnx) Solving 5ln + -1lnx = -2ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 5ln + 2ln + -1lnx = -2ln + 2ln + 2lnx Combine like terms: 5ln + 2ln = 7ln 7ln + -1lnx = -2ln + 2ln + 2lnx Combine like terms: -2ln + 2ln = 0 7ln + -1lnx = 0 + 2lnx 7ln + -1lnx = 2lnx Add '-2lnx' to each side of the equation. 7ln + -1lnx + -2lnx = 2lnx + -2lnx Combine like terms: -1lnx + -2lnx = -3lnx 7ln + -3lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 7ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + -3x) = 0Subproblem 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 '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Add '3x' to each side of the equation. -3x + 3x = -7 + 3x Combine like terms: -3x + 3x = 0 0 = -7 + 3x Simplifying 0 = -7 + 3x 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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