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Simplifying ln(x + -1) + ln(2 + -1x) = ln(6x) Reorder the terms: ln(-1 + x) + ln(2 + -1x) = ln(6x) (-1 * ln + x * ln) + ln(2 + -1x) = ln(6x) (-1ln + lnx) + ln(2 + -1x) = ln(6x) -1ln + lnx + (2 * ln + -1x * ln) = ln(6x) -1ln + lnx + (2ln + -1lnx) = ln(6x) Reorder the terms: -1ln + 2ln + lnx + -1lnx = ln(6x) Combine like terms: -1ln + 2ln = 1ln 1ln + lnx + -1lnx = ln(6x) Combine like terms: lnx + -1lnx = 0 1ln + 0 = ln(6x) 1ln = ln(6x) Remove parenthesis around (6x) 1ln = ln * 6x Reorder the terms for easier multiplication: 1ln = 6ln * x Multiply ln * x 1ln = 6lnx Solving 1ln = 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6lnx' to each side of the equation. 1ln + -6lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 1ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -6x) = 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 + -6x)' equal to zero and attempt to solve: Simplifying 1 + -6x = 0 Solving 1 + -6x = 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 + -6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x = 0 + -1 -6x = 0 + -1 Combine like terms: 0 + -1 = -1 -6x = -1 Add '6x' to each side of the equation. -6x + 6x = -1 + 6x Combine like terms: -6x + 6x = 0 0 = -1 + 6x Simplifying 0 = -1 + 6x 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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