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