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Simplifying -3ln(x + 4) + 3ln(2x) = 0 Reorder the terms: -3ln(4 + x) + 3ln(2x) = 0 (4 * -3ln + x * -3ln) + 3ln(2x) = 0 (-12ln + -3lnx) + 3ln(2x) = 0 Remove parenthesis around (2x) -12ln + -3lnx + 3ln * 2x = 0 Reorder the terms for easier multiplication: -12ln + -3lnx + 3 * 2ln * x = 0 Multiply 3 * 2 -12ln + -3lnx + 6ln * x = 0 Multiply ln * x -12ln + -3lnx + 6lnx = 0 Combine like terms: -3lnx + 6lnx = 3lnx -12ln + 3lnx = 0 Solving -12ln + 3lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-4 + x) = 0 Ignore the factor 3.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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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