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Simplifying 0.5lnx = ln(2x + -1) Reorder the terms: 0.5lnx = ln(-1 + 2x) 0.5lnx = (-1 * ln + 2x * ln) 0.5lnx = (-1ln + 2lnx) Solving 0.5lnx = -1ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. ln + 0.5lnx = -1ln + ln + 2lnx Combine like terms: -1ln + ln = 0 ln + 0.5lnx = 0 + 2lnx ln + 0.5lnx = 2lnx Add '-2lnx' to each side of the equation. ln + 0.5lnx + -2lnx = 2lnx + -2lnx Combine like terms: 0.5lnx + -2lnx = -1.5lnx ln + -1.5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 ln + -1.5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -1.5x) = 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 '(1 + -1.5x)' equal to zero and attempt to solve: Simplifying 1 + -1.5x = 0 Solving 1 + -1.5x = 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 + -1.5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.5x = 0 + -1 -1.5x = 0 + -1 Combine like terms: 0 + -1 = -1 -1.5x = -1 Add '1.5x' to each side of the equation. -1.5x + 1.5x = -1 + 1.5x Combine like terms: -1.5x + 1.5x = 0.0 0.0 = -1 + 1.5x Simplifying 0.0 = -1 + 1.5x 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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