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Simplifying ln(5 + -1x) + ln(-3 + -1x) = ln(1 + -8x) (5 * ln + -1x * ln) + ln(-3 + -1x) = ln(1 + -8x) (5ln + -1lnx) + ln(-3 + -1x) = ln(1 + -8x) 5ln + -1lnx + (-3 * ln + -1x * ln) = ln(1 + -8x) 5ln + -1lnx + (-3ln + -1lnx) = ln(1 + -8x) Reorder the terms: 5ln + -3ln + -1lnx + -1lnx = ln(1 + -8x) Combine like terms: 5ln + -3ln = 2ln 2ln + -1lnx + -1lnx = ln(1 + -8x) Combine like terms: -1lnx + -1lnx = -2lnx 2ln + -2lnx = ln(1 + -8x) 2ln + -2lnx = (1 * ln + -8x * ln) 2ln + -2lnx = (1ln + -8lnx) Solving 2ln + -2lnx = 1ln + -8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. 2ln + -1ln + -2lnx = 1ln + -1ln + -8lnx Combine like terms: 2ln + -1ln = 1ln 1ln + -2lnx = 1ln + -1ln + -8lnx Combine like terms: 1ln + -1ln = 0 1ln + -2lnx = 0 + -8lnx 1ln + -2lnx = -8lnx Add '8lnx' to each side of the equation. 1ln + -2lnx + 8lnx = -8lnx + 8lnx Combine like terms: -2lnx + 8lnx = 6lnx 1ln + 6lnx = -8lnx + 8lnx Combine like terms: -8lnx + 8lnx = 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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