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