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Simplifying ln((5x) + -4) = ln(4) + -1ln(x + -1) Reorder the terms: ln(-4 + (5x)) = ln(4) + -1ln(x + -1) (-4 * ln + (5x) * ln) = ln(4) + -1ln(x + -1) (-4ln + 5lnx) = ln(4) + -1ln(x + -1) Reorder the terms for easier multiplication: -4ln + 5lnx = 4ln + -1ln(x + -1) Reorder the terms: -4ln + 5lnx = 4ln + -1ln(-1 + x) -4ln + 5lnx = 4ln + (-1 * -1ln + x * -1ln) -4ln + 5lnx = 4ln + (1ln + -1lnx) Combine like terms: 4ln + 1ln = 5ln -4ln + 5lnx = 5ln + -1lnx Solving -4ln + 5lnx = 5ln + -1lnx 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 + 5lnx = 5ln + -5ln + -1lnx Combine like terms: -4ln + -5ln = -9ln -9ln + 5lnx = 5ln + -5ln + -1lnx Combine like terms: 5ln + -5ln = 0 -9ln + 5lnx = 0 + -1lnx -9ln + 5lnx = -1lnx Add 'lnx' to each side of the equation. -9ln + 5lnx + lnx = -1lnx + lnx Combine like terms: 5lnx + lnx = 6lnx -9ln + 6lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -9ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-3 + 2x) = 0 Ignore the factor 3.Subproblem 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 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Add '-2x' to each side of the equation. 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 0 = 3 + -2x Simplifying 0 = 3 + -2x 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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