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Simplifying ln(X + 4) = ln(3x + 6) Reorder the terms: ln(4 + X) = ln(3x + 6) (4 * ln + X * ln) = ln(3x + 6) (4ln + lnX) = ln(3x + 6) Reorder the terms: 4ln + lnX = ln(6 + 3x) 4ln + lnX = (6 * ln + 3x * ln) 4ln + lnX = (6ln + 3lnx) Solving 4ln + lnX = 6ln + 3lnx 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. 4ln + -6ln + lnX = 6ln + -6ln + 3lnx Combine like terms: 4ln + -6ln = -2ln -2ln + lnX = 6ln + -6ln + 3lnx Combine like terms: 6ln + -6ln = 0 -2ln + lnX = 0 + 3lnx -2ln + lnX = 3lnx Add '-3lnx' to each side of the equation. -2ln + lnX + -3lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -2ln + lnX + -3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + X + -3x) = 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 '(-2 + X + -3x)' equal to zero and attempt to solve: Simplifying -2 + X + -3x = 0 Solving -2 + X + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + X + 2 + -3x = 0 + 2 Reorder the terms: -2 + 2 + X + -3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + X + -3x = 0 + 2 X + -3x = 0 + 2 Combine like terms: 0 + 2 = 2 X + -3x = 2 Add '-1X' to each side of the equation. X + -1X + -3x = 2 + -1X Combine like terms: X + -1X = 0 0 + -3x = 2 + -1X -3x = 2 + -1X Add '3x' to each side of the equation. -3x + 3x = 2 + -1X + 3x Combine like terms: -3x + 3x = 0 0 = 2 + -1X + 3x Simplifying 0 = 2 + -1X + 3x 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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