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Simplifying ln(3) + 2ln(x) + -1ln(5x) = ln(x + 9) Reorder the terms for easier multiplication: 3ln + 2ln(x) + -1ln(5x) = ln(x + 9) Multiply ln * x 3ln + 2lnx + -1ln(5x) = ln(x + 9) Remove parenthesis around (5x) 3ln + 2lnx + -1ln * 5x = ln(x + 9) Reorder the terms for easier multiplication: 3ln + 2lnx + -1 * 5ln * x = ln(x + 9) Multiply -1 * 5 3ln + 2lnx + -5ln * x = ln(x + 9) Multiply ln * x 3ln + 2lnx + -5lnx = ln(x + 9) Combine like terms: 2lnx + -5lnx = -3lnx 3ln + -3lnx = ln(x + 9) Reorder the terms: 3ln + -3lnx = ln(9 + x) 3ln + -3lnx = (9 * ln + x * ln) 3ln + -3lnx = (9ln + lnx) Solving 3ln + -3lnx = 9ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. 3ln + -9ln + -3lnx = 9ln + -9ln + lnx Combine like terms: 3ln + -9ln = -6ln -6ln + -3lnx = 9ln + -9ln + lnx Combine like terms: 9ln + -9ln = 0 -6ln + -3lnx = 0 + lnx -6ln + -3lnx = lnx Add '-1lnx' to each side of the equation. -6ln + -3lnx + -1lnx = lnx + -1lnx Combine like terms: -3lnx + -1lnx = -4lnx -6ln + -4lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -6ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(3 + 2x) = 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 + 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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