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Simplifying Ln(12) = Ln(ax + b) Reorder the terms for easier multiplication: 12nL = Ln(ax + b) 12nL = (ax * nL + b * nL) 12nL = (anxL + bnL) Solving 12nL = anxL + bnL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1anxL' to each side of the equation. -1anxL + 12nL = anxL + -1anxL + bnL Combine like terms: anxL + -1anxL = 0 -1anxL + 12nL = 0 + bnL -1anxL + 12nL = bnL Add '-1bnL' to each side of the equation. -1anxL + -1bnL + 12nL = bnL + -1bnL Combine like terms: bnL + -1bnL = 0 -1anxL + -1bnL + 12nL = 0 Factor out the Greatest Common Factor (GCF), 'nL'. nL(-1ax + -1b + 12) = 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 '(-1ax + -1b + 12)' equal to zero and attempt to solve: Simplifying -1ax + -1b + 12 = 0 Reorder the terms: 12 + -1ax + -1b = 0 Solving 12 + -1ax + -1b = 0 Move all terms containing n to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -1ax + -12 + -1b = 0 + -12 Reorder the terms: 12 + -12 + -1ax + -1b = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1ax + -1b = 0 + -12 -1ax + -1b = 0 + -12 Combine like terms: 0 + -12 = -12 -1ax + -1b = -12 Add 'ax' to each side of the equation. -1ax + ax + -1b = -12 + ax Combine like terms: -1ax + ax = 0 0 + -1b = -12 + ax -1b = -12 + ax Add 'b' to each side of the equation. -1b + b = -12 + ax + b Combine like terms: -1b + b = 0 0 = -12 + ax + b Simplifying 0 = -12 + ax + b 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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