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Simplifying 2ln(x + 1) = ln(5x + 19) Reorder the terms: 2ln(1 + x) = ln(5x + 19) (1 * 2ln + x * 2ln) = ln(5x + 19) (2ln + 2lnx) = ln(5x + 19) Reorder the terms: 2ln + 2lnx = ln(19 + 5x) 2ln + 2lnx = (19 * ln + 5x * ln) 2ln + 2lnx = (19ln + 5lnx) Solving 2ln + 2lnx = 19ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-19ln' to each side of the equation. 2ln + -19ln + 2lnx = 19ln + -19ln + 5lnx Combine like terms: 2ln + -19ln = -17ln -17ln + 2lnx = 19ln + -19ln + 5lnx Combine like terms: 19ln + -19ln = 0 -17ln + 2lnx = 0 + 5lnx -17ln + 2lnx = 5lnx Add '-5lnx' to each side of the equation. -17ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx -17ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -17ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(17 + 3x) = 0 Ignore the factor -1.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 '(17 + 3x)' equal to zero and attempt to solve: Simplifying 17 + 3x = 0 Solving 17 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 3x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 3x = 0 + -17 3x = 0 + -17 Combine like terms: 0 + -17 = -17 3x = -17 Add '-3x' to each side of the equation. 3x + -3x = -17 + -3x Combine like terms: 3x + -3x = 0 0 = -17 + -3x Simplifying 0 = -17 + -3x 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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