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Simplifying Ln(8x + 2) = Ln(4x + -10) Reorder the terms: nL(2 + 8x) = Ln(4x + -10) (2 * nL + 8x * nL) = Ln(4x + -10) (2nL + 8nxL) = Ln(4x + -10) Reorder the terms: 2nL + 8nxL = nL(-10 + 4x) 2nL + 8nxL = (-10 * nL + 4x * nL) 2nL + 8nxL = (-10nL + 4nxL) Solving 2nL + 8nxL = -10nL + 4nxL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '10nL' to each side of the equation. 2nL + 10nL + 8nxL = -10nL + 10nL + 4nxL Combine like terms: 2nL + 10nL = 12nL 12nL + 8nxL = -10nL + 10nL + 4nxL Combine like terms: -10nL + 10nL = 0 12nL + 8nxL = 0 + 4nxL 12nL + 8nxL = 4nxL Add '-4nxL' to each side of the equation. 12nL + 8nxL + -4nxL = 4nxL + -4nxL Combine like terms: 8nxL + -4nxL = 4nxL 12nL + 4nxL = 4nxL + -4nxL Combine like terms: 4nxL + -4nxL = 0 12nL + 4nxL = 0 Factor out the Greatest Common Factor (GCF), '4nL'. 4nL(3 + x) = 0 Ignore the factor 4.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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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