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Simplifying ln(3 + -2x) + -2ln(x) = ln(5) (3 * ln + -2x * ln) + -2ln(x) = ln(5) (3ln + -2lnx) + -2ln(x) = ln(5) Multiply ln * x 3ln + -2lnx + -2lnx = ln(5) Combine like terms: -2lnx + -2lnx = -4lnx 3ln + -4lnx = ln(5) Reorder the terms for easier multiplication: 3ln + -4lnx = 5ln Solving 3ln + -4lnx = 5ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 3ln + -5ln + -4lnx = 5ln + -5ln Combine like terms: 3ln + -5ln = -2ln -2ln + -4lnx = 5ln + -5ln Combine like terms: 5ln + -5ln = 0 -2ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(1 + 2x) = 0 Ignore the factor -2.Subproblem 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x 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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