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Simplifying Ln(x + 3) + ln(x + -1) = ln(4x + 12) Reorder the terms: nL(3 + x) + ln(x + -1) = ln(4x + 12) (3 * nL + x * nL) + ln(x + -1) = ln(4x + 12) (3nL + nxL) + ln(x + -1) = ln(4x + 12) Reorder the terms: 3nL + nxL + ln(-1 + x) = ln(4x + 12) 3nL + nxL + (-1 * ln + x * ln) = ln(4x + 12) 3nL + nxL + (-1ln + lnx) = ln(4x + 12) Reorder the terms: -1ln + lnx + 3nL + nxL = ln(4x + 12) Reorder the terms: -1ln + lnx + 3nL + nxL = ln(12 + 4x) -1ln + lnx + 3nL + nxL = (12 * ln + 4x * ln) -1ln + lnx + 3nL + nxL = (12ln + 4lnx) Solving -1ln + lnx + 3nL + nxL = 12ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. -1ln + lnx + 3nL + -12ln + nxL = 12ln + -12ln + 4lnx Reorder the terms: -1ln + -12ln + lnx + 3nL + nxL = 12ln + -12ln + 4lnx Combine like terms: -1ln + -12ln = -13ln -13ln + lnx + 3nL + nxL = 12ln + -12ln + 4lnx Combine like terms: 12ln + -12ln = 0 -13ln + lnx + 3nL + nxL = 0 + 4lnx -13ln + lnx + 3nL + nxL = 4lnx Add '-4lnx' to each side of the equation. -13ln + lnx + 3nL + -4lnx + nxL = 4lnx + -4lnx Reorder the terms: -13ln + lnx + -4lnx + 3nL + nxL = 4lnx + -4lnx Combine like terms: lnx + -4lnx = -3lnx -13ln + -3lnx + 3nL + nxL = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -13ln + -3lnx + 3nL + nxL = 0 Add '-3nL' to each side of the equation. -13ln + -3lnx + 3nL + -3nL + nxL = 0 + -3nL Combine like terms: 3nL + -3nL = 0 -13ln + -3lnx + 0 + nxL = 0 + -3nL -13ln + -3lnx + nxL = 0 + -3nL Remove the zero: -13ln + -3lnx + nxL = -3nL Add '-1nxL' to each side of the equation. -13ln + -3lnx + nxL + -1nxL = -3nL + -1nxL Combine like terms: nxL + -1nxL = 0 -13ln + -3lnx + 0 = -3nL + -1nxL -13ln + -3lnx = -3nL + -1nxL Reorder the terms: -13ln + -3lnx + 3nL + nxL = -3nL + 3nL + -1nxL + nxL Combine like terms: -3nL + 3nL = 0 -13ln + -3lnx + 3nL + nxL = 0 + -1nxL + nxL -13ln + -3lnx + 3nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -13ln + -3lnx + 3nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-13l + -3lx + 3L + xL) = 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 '(-13l + -3lx + 3L + xL)' equal to zero and attempt to solve: Simplifying -13l + -3lx + 3L + xL = 0 Reorder the terms: 3L + -13l + -3lx + xL = 0 Solving 3L + -13l + -3lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-3L' to each side of the equation. 3L + -13l + -3lx + -3L + xL = 0 + -3L Reorder the terms: 3L + -3L + -13l + -3lx + xL = 0 + -3L Combine like terms: 3L + -3L = 0 0 + -13l + -3lx + xL = 0 + -3L -13l + -3lx + xL = 0 + -3L Remove the zero: -13l + -3lx + xL = -3L Add '-1xL' to each side of the equation. -13l + -3lx + xL + -1xL = -3L + -1xL Combine like terms: xL + -1xL = 0 -13l + -3lx + 0 = -3L + -1xL -13l + -3lx = -3L + -1xL 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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