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