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