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Simplifying 2ln(4x) = 2ln(8) Remove parenthesis around (4x) 2ln * 4x = 2ln(8) Reorder the terms for easier multiplication: 2 * 4ln * x = 2ln(8) Multiply 2 * 4 8ln * x = 2ln(8) Multiply ln * x 8lnx = 2ln(8) Reorder the terms for easier multiplication: 8lnx = 2 * 8ln Multiply 2 * 8 8lnx = 16ln Solving 8lnx = 16ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-16ln' to each side of the equation. -16ln + 8lnx = 16ln + -16ln Combine like terms: 16ln + -16ln = 0 -16ln + 8lnx = 0 Factor out the Greatest Common Factor (GCF), '8ln'. 8ln(-2 + x) = 0 Ignore the factor 8.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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