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