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Simplifying ln(x + 3) = ln(3x + 5) Reorder the terms: ln(3 + x) = ln(3x + 5) (3 * ln + x * ln) = ln(3x + 5) (3ln + lnx) = ln(3x + 5) Reorder the terms: 3ln + lnx = ln(5 + 3x) 3ln + lnx = (5 * ln + 3x * ln) 3ln + lnx = (5ln + 3lnx) Solving 3ln + lnx = 5ln + 3lnx 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 + 3lnx Combine like terms: 3ln + -5ln = -2ln -2ln + lnx = 5ln + -5ln + 3lnx Combine like terms: 5ln + -5ln = 0 -2ln + lnx = 0 + 3lnx -2ln + lnx = 3lnx Add '-3lnx' to each side of the equation. -2ln + lnx + -3lnx = 3lnx + -3lnx Combine like terms: lnx + -3lnx = -2lnx -2ln + -2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -2ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(1 + 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 '(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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