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