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Simplifying Ln(3 + -1x) + ln(-2 + -1x) = ln(3 + -9x) (3 * nL + -1x * nL) + ln(-2 + -1x) = ln(3 + -9x) (3nL + -1nxL) + ln(-2 + -1x) = ln(3 + -9x) 3nL + -1nxL + (-2 * ln + -1x * ln) = ln(3 + -9x) 3nL + -1nxL + (-2ln + -1lnx) = ln(3 + -9x) Reorder the terms: -2ln + -1lnx + 3nL + -1nxL = ln(3 + -9x) -2ln + -1lnx + 3nL + -1nxL = (3 * ln + -9x * ln) -2ln + -1lnx + 3nL + -1nxL = (3ln + -9lnx) Solving -2ln + -1lnx + 3nL + -1nxL = 3ln + -9lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3ln' to each side of the equation. -2ln + -1lnx + 3nL + -3ln + -1nxL = 3ln + -3ln + -9lnx Reorder the terms: -2ln + -3ln + -1lnx + 3nL + -1nxL = 3ln + -3ln + -9lnx Combine like terms: -2ln + -3ln = -5ln -5ln + -1lnx + 3nL + -1nxL = 3ln + -3ln + -9lnx Combine like terms: 3ln + -3ln = 0 -5ln + -1lnx + 3nL + -1nxL = 0 + -9lnx -5ln + -1lnx + 3nL + -1nxL = -9lnx Add '9lnx' to each side of the equation. -5ln + -1lnx + 3nL + 9lnx + -1nxL = -9lnx + 9lnx Reorder the terms: -5ln + -1lnx + 9lnx + 3nL + -1nxL = -9lnx + 9lnx Combine like terms: -1lnx + 9lnx = 8lnx -5ln + 8lnx + 3nL + -1nxL = -9lnx + 9lnx Combine like terms: -9lnx + 9lnx = 0 -5ln + 8lnx + 3nL + -1nxL = 0 Add '-3nL' to each side of the equation. -5ln + 8lnx + 3nL + -3nL + -1nxL = 0 + -3nL Combine like terms: 3nL + -3nL = 0 -5ln + 8lnx + 0 + -1nxL = 0 + -3nL -5ln + 8lnx + -1nxL = 0 + -3nL Remove the zero: -5ln + 8lnx + -1nxL = -3nL Add 'nxL' to each side of the equation. -5ln + 8lnx + -1nxL + nxL = -3nL + nxL Combine like terms: -1nxL + nxL = 0 -5ln + 8lnx + 0 = -3nL + nxL -5ln + 8lnx = -3nL + nxL Reorder the terms: -5ln + 8lnx + 3nL + -1nxL = -3nL + 3nL + nxL + -1nxL Combine like terms: -3nL + 3nL = 0 -5ln + 8lnx + 3nL + -1nxL = 0 + nxL + -1nxL -5ln + 8lnx + 3nL + -1nxL = nxL + -1nxL Combine like terms: nxL + -1nxL = 0 -5ln + 8lnx + 3nL + -1nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-5l + 8lx + 3L + -1xL) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(-5l + 8lx + 3L + -1xL)' equal to zero and attempt to solve: Simplifying -5l + 8lx + 3L + -1xL = 0 Reorder the terms: 3L + -5l + 8lx + -1xL = 0 Solving 3L + -5l + 8lx + -1xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-3L' to each side of the equation. 3L + -5l + 8lx + -3L + -1xL = 0 + -3L Reorder the terms: 3L + -3L + -5l + 8lx + -1xL = 0 + -3L Combine like terms: 3L + -3L = 0 0 + -5l + 8lx + -1xL = 0 + -3L -5l + 8lx + -1xL = 0 + -3L Remove the zero: -5l + 8lx + -1xL = -3L Add 'xL' to each side of the equation. -5l + 8lx + -1xL + xL = -3L + xL Combine like terms: -1xL + xL = 0 -5l + 8lx + 0 = -3L + xL -5l + 8lx = -3L + xL 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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