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Simplifying 2ln(2x + -1) + lnx = ln(6x + -3) Reorder the terms: 2ln(-1 + 2x) + lnx = ln(6x + -3) (-1 * 2ln + 2x * 2ln) + lnx = ln(6x + -3) (-2ln + 4lnx) + lnx = ln(6x + -3) Combine like terms: 4lnx + lnx = 5lnx -2ln + 5lnx = ln(6x + -3) Reorder the terms: -2ln + 5lnx = ln(-3 + 6x) -2ln + 5lnx = (-3 * ln + 6x * ln) -2ln + 5lnx = (-3ln + 6lnx) Solving -2ln + 5lnx = -3ln + 6lnx 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 + 5lnx = -3ln + 3ln + 6lnx Combine like terms: -2ln + 3ln = 1ln 1ln + 5lnx = -3ln + 3ln + 6lnx Combine like terms: -3ln + 3ln = 0 1ln + 5lnx = 0 + 6lnx 1ln + 5lnx = 6lnx Add '-6lnx' to each side of the equation. 1ln + 5lnx + -6lnx = 6lnx + -6lnx Combine like terms: 5lnx + -6lnx = -1lnx 1ln + -1lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 1ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + 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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