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