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