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Simplifying ln(15x) + -2ln(1 + x) = ln(3) Remove parenthesis around (15x) ln * 15x + -2ln(1 + x) = ln(3) Reorder the terms for easier multiplication: 15ln * x + -2ln(1 + x) = ln(3) Multiply ln * x 15lnx + -2ln(1 + x) = ln(3) 15lnx + (1 * -2ln + x * -2ln) = ln(3) 15lnx + (-2ln + -2lnx) = ln(3) Reorder the terms: -2ln + 15lnx + -2lnx = ln(3) Combine like terms: 15lnx + -2lnx = 13lnx -2ln + 13lnx = ln(3) Reorder the terms for easier multiplication: -2ln + 13lnx = 3ln Solving -2ln + 13lnx = 3ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. -2ln + -3ln + 13lnx = 3ln + -3ln Combine like terms: -2ln + -3ln = -5ln -5ln + 13lnx = 3ln + -3ln Combine like terms: 3ln + -3ln = 0 -5ln + 13lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-5 + 13x) = 0Subproblem 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 '(-5 + 13x)' equal to zero and attempt to solve: Simplifying -5 + 13x = 0 Solving -5 + 13x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 13x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 13x = 0 + 5 13x = 0 + 5 Combine like terms: 0 + 5 = 5 13x = 5 Add '-13x' to each side of the equation. 13x + -13x = 5 + -13x Combine like terms: 13x + -13x = 0 0 = 5 + -13x Simplifying 0 = 5 + -13x 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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