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Simplifying Ln(x + -5) = Ln(4x + 2) Reorder the terms: nL(-5 + x) = Ln(4x + 2) (-5 * nL + x * nL) = Ln(4x + 2) (-5nL + nxL) = Ln(4x + 2) Reorder the terms: -5nL + nxL = nL(2 + 4x) -5nL + nxL = (2 * nL + 4x * nL) -5nL + nxL = (2nL + 4nxL) Solving -5nL + nxL = 2nL + 4nxL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2nL' to each side of the equation. -5nL + -2nL + nxL = 2nL + -2nL + 4nxL Combine like terms: -5nL + -2nL = -7nL -7nL + nxL = 2nL + -2nL + 4nxL Combine like terms: 2nL + -2nL = 0 -7nL + nxL = 0 + 4nxL -7nL + nxL = 4nxL Add '-4nxL' to each side of the equation. -7nL + nxL + -4nxL = 4nxL + -4nxL Combine like terms: nxL + -4nxL = -3nxL -7nL + -3nxL = 4nxL + -4nxL Combine like terms: 4nxL + -4nxL = 0 -7nL + -3nxL = 0 Factor out the Greatest Common Factor (GCF), '-1nL'. -1nL(7 + 3x) = 0 Ignore the factor -1.Subproblem 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 '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Add '-3x' to each side of the equation. 3x + -3x = -7 + -3x Combine like terms: 3x + -3x = 0 0 = -7 + -3x Simplifying 0 = -7 + -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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