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