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