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Simplifying Ln(X + -4) + ln(x + 3) = ln(6) Reorder the terms: nL(-4 + X) + ln(x + 3) = ln(6) (-4 * nL + X * nL) + ln(x + 3) = ln(6) (-4nL + nLX) + ln(x + 3) = ln(6) Reorder the terms: -4nL + nLX + ln(3 + x) = ln(6) -4nL + nLX + (3 * ln + x * ln) = ln(6) -4nL + nLX + (3ln + lnx) = ln(6) Reorder the terms: 3ln + lnx + -4nL + nLX = ln(6) Reorder the terms for easier multiplication: 3ln + lnx + -4nL + nLX = 6ln Solving 3ln + lnx + -4nL + nLX = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 3ln + lnx + -4nL + -6ln + nLX = 6ln + -6ln Reorder the terms: 3ln + -6ln + lnx + -4nL + nLX = 6ln + -6ln Combine like terms: 3ln + -6ln = -3ln -3ln + lnx + -4nL + nLX = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -3ln + lnx + -4nL + nLX = 0 Add '4nL' to each side of the equation. -3ln + lnx + -4nL + 4nL + nLX = 0 + 4nL Combine like terms: -4nL + 4nL = 0 -3ln + lnx + 0 + nLX = 0 + 4nL -3ln + lnx + nLX = 0 + 4nL Remove the zero: -3ln + lnx + nLX = 4nL Add '-1nLX' to each side of the equation. -3ln + lnx + nLX + -1nLX = 4nL + -1nLX Combine like terms: nLX + -1nLX = 0 -3ln + lnx + 0 = 4nL + -1nLX -3ln + lnx = 4nL + -1nLX Reorder the terms: -3ln + lnx + -4nL + nLX = 4nL + -4nL + -1nLX + nLX Combine like terms: 4nL + -4nL = 0 -3ln + lnx + -4nL + nLX = 0 + -1nLX + nLX -3ln + lnx + -4nL + nLX = -1nLX + nLX Combine like terms: -1nLX + nLX = 0 -3ln + lnx + -4nL + nLX = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-3l + lx + -4L + LX) = 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 '(-3l + lx + -4L + LX)' equal to zero and attempt to solve: Simplifying -3l + lx + -4L + LX = 0 Reorder the terms: -4L + LX + -3l + lx = 0 Solving -4L + LX + -3l + lx = 0 Move all terms containing l to the left, all other terms to the right. Add '4L' to each side of the equation. -4L + LX + -3l + 4L + lx = 0 + 4L Reorder the terms: -4L + 4L + LX + -3l + lx = 0 + 4L Combine like terms: -4L + 4L = 0 0 + LX + -3l + lx = 0 + 4L LX + -3l + lx = 0 + 4L Remove the zero: LX + -3l + lx = 4L Add '-1LX' to each side of the equation. LX + -3l + -1LX + lx = 4L + -1LX Reorder the terms: LX + -1LX + -3l + lx = 4L + -1LX Combine like terms: LX + -1LX = 0 0 + -3l + lx = 4L + -1LX -3l + lx = 4L + -1LX 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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