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Simplifying ln(8x) + -2ln(x2) = ln(4) Remove parenthesis around (8x) ln * 8x + -2ln(x2) = ln(4) Reorder the terms for easier multiplication: 8ln * x + -2ln(x2) = ln(4) Multiply ln * x 8lnx + -2ln(x2) = ln(4) Multiply ln * x2 8lnx + -2lnx2 = ln(4) Reorder the terms for easier multiplication: 8lnx + -2lnx2 = 4ln Solving 8lnx + -2lnx2 = 4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 8lnx + -4ln + -2lnx2 = 4ln + -4ln Reorder the terms: -4ln + 8lnx + -2lnx2 = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -4ln + 8lnx + -2lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-2 + 4x + -1x2) = 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 '(-2 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + 4x + -1x2 = 0 Solving -2 + 4x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 4x + 2 + -1x2 = 0 + 2 Reorder the terms: -2 + 2 + 4x + -1x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4x + -1x2 = 0 + 2 4x + -1x2 = 0 + 2 Combine like terms: 0 + 2 = 2 4x + -1x2 = 2 Add '-4x' to each side of the equation. 4x + -4x + -1x2 = 2 + -4x Combine like terms: 4x + -4x = 0 0 + -1x2 = 2 + -4x -1x2 = 2 + -4x Add 'x2' to each side of the equation. -1x2 + x2 = 2 + -4x + x2 Combine like terms: -1x2 + x2 = 0 0 = 2 + -4x + x2 Simplifying 0 = 2 + -4x + x2 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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