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