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Simplifying ln(6 + -1x) + -1ln(-4 + -1x) = ln(1 + -8x) (6 * ln + -1x * ln) + -1ln(-4 + -1x) = ln(1 + -8x) (6ln + -1lnx) + -1ln(-4 + -1x) = ln(1 + -8x) 6ln + -1lnx + (-4 * -1ln + -1x * -1ln) = ln(1 + -8x) 6ln + -1lnx + (4ln + 1lnx) = ln(1 + -8x) Reorder the terms: 6ln + 4ln + -1lnx + 1lnx = ln(1 + -8x) Combine like terms: 6ln + 4ln = 10ln 10ln + -1lnx + 1lnx = ln(1 + -8x) Combine like terms: -1lnx + 1lnx = 0 10ln + 0 = ln(1 + -8x) 10ln = ln(1 + -8x) 10ln = (1 * ln + -8x * ln) 10ln = (1ln + -8lnx) Solving 10ln = 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. 10ln + -1ln = 1ln + -1ln + -8lnx Combine like terms: 10ln + -1ln = 9ln 9ln = 1ln + -1ln + -8lnx Combine like terms: 1ln + -1ln = 0 9ln = 0 + -8lnx 9ln = -8lnx Add '8lnx' to each side of the equation. 9ln + 8lnx = -8lnx + 8lnx Combine like terms: -8lnx + 8lnx = 0 9ln + 8lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + 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 '(9 + 8x)' equal to zero and attempt to solve: Simplifying 9 + 8x = 0 Solving 9 + 8x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 8x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8x = 0 + -9 8x = 0 + -9 Combine like terms: 0 + -9 = -9 8x = -9 Add '-8x' to each side of the equation. 8x + -8x = -9 + -8x Combine like terms: 8x + -8x = 0 0 = -9 + -8x Simplifying 0 = -9 + -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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