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Simplifying 2ln(x + -4) = ln(8x) Reorder the terms: 2ln(-4 + x) = ln(8x) (-4 * 2ln + x * 2ln) = ln(8x) (-8ln + 2lnx) = ln(8x) Remove parenthesis around (8x) -8ln + 2lnx = ln * 8x Reorder the terms for easier multiplication: -8ln + 2lnx = 8ln * x Multiply ln * x -8ln + 2lnx = 8lnx Solving -8ln + 2lnx = 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8lnx' to each side of the equation. -8ln + 2lnx + -8lnx = 8lnx + -8lnx Combine like terms: 2lnx + -8lnx = -6lnx -8ln + -6lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 -8ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(4 + 3x) = 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 '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 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 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Add '-3x' to each side of the equation. 3x + -3x = -4 + -3x Combine like terms: 3x + -3x = 0 0 = -4 + -3x Simplifying 0 = -4 + -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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