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Simplifying 2ln(x + 2) + lnx = ln(13x + 6) Reorder the terms: 2ln(2 + x) + lnx = ln(13x + 6) (2 * 2ln + x * 2ln) + lnx = ln(13x + 6) (4ln + 2lnx) + lnx = ln(13x + 6) Combine like terms: 2lnx + lnx = 3lnx 4ln + 3lnx = ln(13x + 6) Reorder the terms: 4ln + 3lnx = ln(6 + 13x) 4ln + 3lnx = (6 * ln + 13x * ln) 4ln + 3lnx = (6ln + 13lnx) Solving 4ln + 3lnx = 6ln + 13lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 4ln + -6ln + 3lnx = 6ln + -6ln + 13lnx Combine like terms: 4ln + -6ln = -2ln -2ln + 3lnx = 6ln + -6ln + 13lnx Combine like terms: 6ln + -6ln = 0 -2ln + 3lnx = 0 + 13lnx -2ln + 3lnx = 13lnx Add '-13lnx' to each side of the equation. -2ln + 3lnx + -13lnx = 13lnx + -13lnx Combine like terms: 3lnx + -13lnx = -10lnx -2ln + -10lnx = 13lnx + -13lnx Combine like terms: 13lnx + -13lnx = 0 -2ln + -10lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(1 + 5x) = 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 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Add '-5x' to each side of the equation. 5x + -5x = -1 + -5x Combine like terms: 5x + -5x = 0 0 = -1 + -5x Simplifying 0 = -1 + -5x 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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