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Simplifying Ln(3x + -1) = Ln(-2x + 5) Reorder the terms: nL(-1 + 3x) = Ln(-2x + 5) (-1 * nL + 3x * nL) = Ln(-2x + 5) (-1nL + 3nxL) = Ln(-2x + 5) Reorder the terms: -1nL + 3nxL = nL(5 + -2x) -1nL + 3nxL = (5 * nL + -2x * nL) -1nL + 3nxL = (5nL + -2nxL) Solving -1nL + 3nxL = 5nL + -2nxL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5nL' to each side of the equation. -1nL + -5nL + 3nxL = 5nL + -5nL + -2nxL Combine like terms: -1nL + -5nL = -6nL -6nL + 3nxL = 5nL + -5nL + -2nxL Combine like terms: 5nL + -5nL = 0 -6nL + 3nxL = 0 + -2nxL -6nL + 3nxL = -2nxL Add '2nxL' to each side of the equation. -6nL + 3nxL + 2nxL = -2nxL + 2nxL Combine like terms: 3nxL + 2nxL = 5nxL -6nL + 5nxL = -2nxL + 2nxL Combine like terms: -2nxL + 2nxL = 0 -6nL + 5nxL = 0 Factor out the Greatest Common Factor (GCF), 'nL'. nL(-6 + 5x) = 0Subproblem 1
Set the factor 'nL' equal to zero and attempt to solve: Simplifying nL = 0 Solving nL = 0 Move all terms containing n to the left, all other terms to the right. Simplifying nL = 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 '(-6 + 5x)' equal to zero and attempt to solve: Simplifying -6 + 5x = 0 Solving -6 + 5x = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5x = 0 + 6 5x = 0 + 6 Combine like terms: 0 + 6 = 6 5x = 6 Add '-5x' to each side of the equation. 5x + -5x = 6 + -5x Combine like terms: 5x + -5x = 0 0 = 6 + -5x Simplifying 0 = 6 + -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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