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Simplifying 2ln(x) = 4ln(3) + 2 Multiply ln * x 2lnx = 4ln(3) + 2 Reorder the terms for easier multiplication: 2lnx = 4 * 3ln + 2 Multiply 4 * 3 2lnx = 12ln + 2 Reorder the terms: 2lnx = 2 + 12ln Solving 2lnx = 2 + 12ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. -12ln + 2lnx = 2 + 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -12ln + 2lnx = 2 + 0 -12ln + 2lnx = 2 Reorder the terms: -2 + -12ln + 2lnx = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -12ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -6ln + lnx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -6ln + lnx)' equal to zero and attempt to solve: Simplifying -1 + -6ln + lnx = 0 Solving -1 + -6ln + lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -6ln + 1 + lnx = 0 + 1 Reorder the terms: -1 + 1 + -6ln + lnx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6ln + lnx = 0 + 1 -6ln + lnx = 0 + 1 Combine like terms: 0 + 1 = 1 -6ln + lnx = 1 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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