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