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Simplifying ln(4x + -1) = ln(5) + -1ln(x + -5) Reorder the terms: ln(-1 + 4x) = ln(5) + -1ln(x + -5) (-1 * ln + 4x * ln) = ln(5) + -1ln(x + -5) (-1ln + 4lnx) = ln(5) + -1ln(x + -5) Reorder the terms for easier multiplication: -1ln + 4lnx = 5ln + -1ln(x + -5) Reorder the terms: -1ln + 4lnx = 5ln + -1ln(-5 + x) -1ln + 4lnx = 5ln + (-5 * -1ln + x * -1ln) -1ln + 4lnx = 5ln + (5ln + -1lnx) Combine like terms: 5ln + 5ln = 10ln -1ln + 4lnx = 10ln + -1lnx Solving -1ln + 4lnx = 10ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -1ln + -10ln + 4lnx = 10ln + -10ln + -1lnx Combine like terms: -1ln + -10ln = -11ln -11ln + 4lnx = 10ln + -10ln + -1lnx Combine like terms: 10ln + -10ln = 0 -11ln + 4lnx = 0 + -1lnx -11ln + 4lnx = -1lnx Add 'lnx' to each side of the equation. -11ln + 4lnx + lnx = -1lnx + lnx Combine like terms: 4lnx + lnx = 5lnx -11ln + 5lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -11ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-11 + 5x) = 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 '(-11 + 5x)' equal to zero and attempt to solve: Simplifying -11 + 5x = 0 Solving -11 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 5x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 5x = 0 + 11 5x = 0 + 11 Combine like terms: 0 + 11 = 11 5x = 11 Add '-5x' to each side of the equation. 5x + -5x = 11 + -5x Combine like terms: 5x + -5x = 0 0 = 11 + -5x Simplifying 0 = 11 + -5x 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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