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Simplifying 2ln(x) = ln(2) + ln(3x + -4) Multiply ln * x 2lnx = ln(2) + ln(3x + -4) Reorder the terms for easier multiplication: 2lnx = 2ln + ln(3x + -4) Reorder the terms: 2lnx = 2ln + ln(-4 + 3x) 2lnx = 2ln + (-4 * ln + 3x * ln) 2lnx = 2ln + (-4ln + 3lnx) Combine like terms: 2ln + -4ln = -2ln 2lnx = -2ln + 3lnx Solving 2lnx = -2ln + 3lnx 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 + 2ln + 3lnx Combine like terms: -2ln + 2ln = 0 2ln + 2lnx = 0 + 3lnx 2ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. 2ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx 2ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 2ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(2 + -1x) = 0Subproblem 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 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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