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Simplifying 2ln(x + 3) = ln(5x + 29) Reorder the terms: 2ln(3 + x) = ln(5x + 29) (3 * 2ln + x * 2ln) = ln(5x + 29) (6ln + 2lnx) = ln(5x + 29) Reorder the terms: 6ln + 2lnx = ln(29 + 5x) 6ln + 2lnx = (29 * ln + 5x * ln) 6ln + 2lnx = (29ln + 5lnx) Solving 6ln + 2lnx = 29ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-29ln' to each side of the equation. 6ln + -29ln + 2lnx = 29ln + -29ln + 5lnx Combine like terms: 6ln + -29ln = -23ln -23ln + 2lnx = 29ln + -29ln + 5lnx Combine like terms: 29ln + -29ln = 0 -23ln + 2lnx = 0 + 5lnx -23ln + 2lnx = 5lnx Add '-5lnx' to each side of the equation. -23ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx -23ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -23ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(23 + 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 '(23 + 3x)' equal to zero and attempt to solve: Simplifying 23 + 3x = 0 Solving 23 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 3x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 3x = 0 + -23 3x = 0 + -23 Combine like terms: 0 + -23 = -23 3x = -23 Add '-3x' to each side of the equation. 3x + -3x = -23 + -3x Combine like terms: 3x + -3x = 0 0 = -23 + -3x Simplifying 0 = -23 + -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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