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Simplifying 2ln(x + 3) = ln(4x + 17) Reorder the terms: 2ln(3 + x) = ln(4x + 17) (3 * 2ln + x * 2ln) = ln(4x + 17) (6ln + 2lnx) = ln(4x + 17) Reorder the terms: 6ln + 2lnx = ln(17 + 4x) 6ln + 2lnx = (17 * ln + 4x * ln) 6ln + 2lnx = (17ln + 4lnx) Solving 6ln + 2lnx = 17ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-17ln' to each side of the equation. 6ln + -17ln + 2lnx = 17ln + -17ln + 4lnx Combine like terms: 6ln + -17ln = -11ln -11ln + 2lnx = 17ln + -17ln + 4lnx Combine like terms: 17ln + -17ln = 0 -11ln + 2lnx = 0 + 4lnx -11ln + 2lnx = 4lnx Add '-4lnx' to each side of the equation. -11ln + 2lnx + -4lnx = 4lnx + -4lnx Combine like terms: 2lnx + -4lnx = -2lnx -11ln + -2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -11ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(11 + 2x) = 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 '(11 + 2x)' equal to zero and attempt to solve: Simplifying 11 + 2x = 0 Solving 11 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 2x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 2x = 0 + -11 2x = 0 + -11 Combine like terms: 0 + -11 = -11 2x = -11 Add '-2x' to each side of the equation. 2x + -2x = -11 + -2x Combine like terms: 2x + -2x = 0 0 = -11 + -2x Simplifying 0 = -11 + -2x 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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