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Simplifying 2ln(x + 3) = ln(5x + 21) Reorder the terms: 2ln(3 + x) = ln(5x + 21) (3 * 2ln + x * 2ln) = ln(5x + 21) (6ln + 2lnx) = ln(5x + 21) Reorder the terms: 6ln + 2lnx = ln(21 + 5x) 6ln + 2lnx = (21 * ln + 5x * ln) 6ln + 2lnx = (21ln + 5lnx) Solving 6ln + 2lnx = 21ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-21ln' to each side of the equation. 6ln + -21ln + 2lnx = 21ln + -21ln + 5lnx Combine like terms: 6ln + -21ln = -15ln -15ln + 2lnx = 21ln + -21ln + 5lnx Combine like terms: 21ln + -21ln = 0 -15ln + 2lnx = 0 + 5lnx -15ln + 2lnx = 5lnx Add '-5lnx' to each side of the equation. -15ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx -15ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -15ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-3ln'. -3ln(5 + x) = 0 Ignore the factor -3.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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -1x 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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