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Simplifying ln(x) + ln(2 + -2x) = ln(3 + -5x) Multiply ln * x lnx + ln(2 + -2x) = ln(3 + -5x) lnx + (2 * ln + -2x * ln) = ln(3 + -5x) lnx + (2ln + -2lnx) = ln(3 + -5x) Reorder the terms: 2ln + lnx + -2lnx = ln(3 + -5x) Combine like terms: lnx + -2lnx = -1lnx 2ln + -1lnx = ln(3 + -5x) 2ln + -1lnx = (3 * ln + -5x * ln) 2ln + -1lnx = (3ln + -5lnx) Solving 2ln + -1lnx = 3ln + -5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. 2ln + -3ln + -1lnx = 3ln + -3ln + -5lnx Combine like terms: 2ln + -3ln = -1ln -1ln + -1lnx = 3ln + -3ln + -5lnx Combine like terms: 3ln + -3ln = 0 -1ln + -1lnx = 0 + -5lnx -1ln + -1lnx = -5lnx Add '5lnx' to each side of the equation. -1ln + -1lnx + 5lnx = -5lnx + 5lnx Combine like terms: -1lnx + 5lnx = 4lnx -1ln + 4lnx = -5lnx + 5lnx Combine like terms: -5lnx + 5lnx = 0 -1ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1 + 4x) = 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 + 4x)' equal to zero and attempt to solve: Simplifying -1 + 4x = 0 Solving -1 + 4x = 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 + 4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4x = 0 + 1 4x = 0 + 1 Combine like terms: 0 + 1 = 1 4x = 1 Add '-4x' to each side of the equation. 4x + -4x = 1 + -4x Combine like terms: 4x + -4x = 0 0 = 1 + -4x Simplifying 0 = 1 + -4x 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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