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