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