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Simplifying ln(1 + -1x) + ln(2 + -1x) = ln(6x) (1 * ln + -1x * ln) + ln(2 + -1x) = ln(6x) (1ln + -1lnx) + ln(2 + -1x) = ln(6x) 1ln + -1lnx + (2 * ln + -1x * ln) = ln(6x) 1ln + -1lnx + (2ln + -1lnx) = ln(6x) Reorder the terms: 1ln + 2ln + -1lnx + -1lnx = ln(6x) Combine like terms: 1ln + 2ln = 3ln 3ln + -1lnx + -1lnx = ln(6x) Combine like terms: -1lnx + -1lnx = -2lnx 3ln + -2lnx = ln(6x) Remove parenthesis around (6x) 3ln + -2lnx = ln * 6x Reorder the terms for easier multiplication: 3ln + -2lnx = 6ln * x Multiply ln * x 3ln + -2lnx = 6lnx Solving 3ln + -2lnx = 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. 3ln + -2lnx + -6lnx = 6lnx + -6lnx Combine like terms: -2lnx + -6lnx = -8lnx 3ln + -8lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 3ln + -8lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + -8x) = 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 '(3 + -8x)' equal to zero and attempt to solve: Simplifying 3 + -8x = 0 Solving 3 + -8x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x = 0 + -3 -8x = 0 + -3 Combine like terms: 0 + -3 = -3 -8x = -3 Add '8x' to each side of the equation. -8x + 8x = -3 + 8x Combine like terms: -8x + 8x = 0 0 = -3 + 8x Simplifying 0 = -3 + 8x 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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