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Simplifying ln(32x2) + -4ln(x) = ln(2) Remove parenthesis around (32x2) ln * 32x2 + -4ln(x) = ln(2) Reorder the terms for easier multiplication: 32ln * x2 + -4ln(x) = ln(2) Multiply ln * x2 32lnx2 + -4ln(x) = ln(2) Multiply ln * x 32lnx2 + -4lnx = ln(2) Reorder the terms: -4lnx + 32lnx2 = ln(2) Reorder the terms for easier multiplication: -4lnx + 32lnx2 = 2ln Solving -4lnx + 32lnx2 = 2ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. -4lnx + -2ln + 32lnx2 = 2ln + -2ln Reorder the terms: -2ln + -4lnx + 32lnx2 = 2ln + -2ln Combine like terms: 2ln + -2ln = 0 -2ln + -4lnx + 32lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-1 + -2x + 16x2) = 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 '(-1 + -2x + 16x2)' equal to zero and attempt to solve: Simplifying -1 + -2x + 16x2 = 0 Solving -1 + -2x + 16x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -2x + 1 + 16x2 = 0 + 1 Reorder the terms: -1 + 1 + -2x + 16x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x + 16x2 = 0 + 1 -2x + 16x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2x + 16x2 = 1 Add '2x' to each side of the equation. -2x + 2x + 16x2 = 1 + 2x Combine like terms: -2x + 2x = 0 0 + 16x2 = 1 + 2x 16x2 = 1 + 2x Add '-16x2' to each side of the equation. 16x2 + -16x2 = 1 + 2x + -16x2 Combine like terms: 16x2 + -16x2 = 0 0 = 1 + 2x + -16x2 Simplifying 0 = 1 + 2x + -16x2 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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