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