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