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Simplifying ln(4x + 9) = ln(2x + 3) Reorder the terms: ln(9 + 4x) = ln(2x + 3) (9 * ln + 4x * ln) = ln(2x + 3) (9ln + 4lnx) = ln(2x + 3) Reorder the terms: 9ln + 4lnx = ln(3 + 2x) 9ln + 4lnx = (3 * ln + 2x * ln) 9ln + 4lnx = (3ln + 2lnx) Solving 9ln + 4lnx = 3ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 9ln + -3ln + 4lnx = 3ln + -3ln + 2lnx Combine like terms: 9ln + -3ln = 6ln 6ln + 4lnx = 3ln + -3ln + 2lnx Combine like terms: 3ln + -3ln = 0 6ln + 4lnx = 0 + 2lnx 6ln + 4lnx = 2lnx Add '-2lnx' to each side of the equation. 6ln + 4lnx + -2lnx = 2lnx + -2lnx Combine like terms: 4lnx + -2lnx = 2lnx 6ln + 2lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 6ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(3 + x) = 0 Ignore the factor 2.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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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