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Simplifying ln(-1x + 1) + -1ln(3x + 5) = ln(-6 + 1) Reorder the terms: ln(1 + -1x) + -1ln(3x + 5) = ln(-6 + 1) (1 * ln + -1x * ln) + -1ln(3x + 5) = ln(-6 + 1) (1ln + -1lnx) + -1ln(3x + 5) = ln(-6 + 1) Reorder the terms: 1ln + -1lnx + -1ln(5 + 3x) = ln(-6 + 1) 1ln + -1lnx + (5 * -1ln + 3x * -1ln) = ln(-6 + 1) 1ln + -1lnx + (-5ln + -3lnx) = ln(-6 + 1) Reorder the terms: 1ln + -5ln + -1lnx + -3lnx = ln(-6 + 1) Combine like terms: 1ln + -5ln = -4ln -4ln + -1lnx + -3lnx = ln(-6 + 1) Combine like terms: -1lnx + -3lnx = -4lnx -4ln + -4lnx = ln(-6 + 1) Combine like terms: -6 + 1 = -5 -4ln + -4lnx = ln(-5) Reorder the terms for easier multiplication: -4ln + -4lnx = -5ln Solving -4ln + -4lnx = -5ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. -4ln + 5ln + -4lnx = -5ln + 5ln Combine like terms: -4ln + 5ln = 1ln 1ln + -4lnx = -5ln + 5ln Combine like terms: -5ln + 5ln = 0 1ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -4x) = 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 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Add '4x' to each side of the equation. -4x + 4x = -1 + 4x Combine like terms: -4x + 4x = 0 0 = -1 + 4x Simplifying 0 = -1 + 4x 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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