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Simplifying Ln(x + -9) + -1ln(x + 7) = ln(x + -2) + -1ln(x + 4) Reorder the terms: nL(-9 + x) + -1ln(x + 7) = ln(x + -2) + -1ln(x + 4) (-9 * nL + x * nL) + -1ln(x + 7) = ln(x + -2) + -1ln(x + 4) (-9nL + nxL) + -1ln(x + 7) = ln(x + -2) + -1ln(x + 4) Reorder the terms: -9nL + nxL + -1ln(7 + x) = ln(x + -2) + -1ln(x + 4) -9nL + nxL + (7 * -1ln + x * -1ln) = ln(x + -2) + -1ln(x + 4) -9nL + nxL + (-7ln + -1lnx) = ln(x + -2) + -1ln(x + 4) Reorder the terms: -7ln + -1lnx + -9nL + nxL = ln(x + -2) + -1ln(x + 4) Reorder the terms: -7ln + -1lnx + -9nL + nxL = ln(-2 + x) + -1ln(x + 4) -7ln + -1lnx + -9nL + nxL = (-2 * ln + x * ln) + -1ln(x + 4) -7ln + -1lnx + -9nL + nxL = (-2ln + lnx) + -1ln(x + 4) Reorder the terms: -7ln + -1lnx + -9nL + nxL = -2ln + lnx + -1ln(4 + x) -7ln + -1lnx + -9nL + nxL = -2ln + lnx + (4 * -1ln + x * -1ln) -7ln + -1lnx + -9nL + nxL = -2ln + lnx + (-4ln + -1lnx) Reorder the terms: -7ln + -1lnx + -9nL + nxL = -2ln + -4ln + lnx + -1lnx Combine like terms: -2ln + -4ln = -6ln -7ln + -1lnx + -9nL + nxL = -6ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -7ln + -1lnx + -9nL + nxL = -6ln + 0 -7ln + -1lnx + -9nL + nxL = -6ln Solving -7ln + -1lnx + -9nL + nxL = -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. -7ln + -1lnx + -9nL + 6ln + nxL = -6ln + 6ln Reorder the terms: -7ln + 6ln + -1lnx + -9nL + nxL = -6ln + 6ln Combine like terms: -7ln + 6ln = -1ln -1ln + -1lnx + -9nL + nxL = -6ln + 6ln Combine like terms: -6ln + 6ln = 0 -1ln + -1lnx + -9nL + nxL = 0 Add '9nL' to each side of the equation. -1ln + -1lnx + -9nL + 9nL + nxL = 0 + 9nL Combine like terms: -9nL + 9nL = 0 -1ln + -1lnx + 0 + nxL = 0 + 9nL -1ln + -1lnx + nxL = 0 + 9nL Remove the zero: -1ln + -1lnx + nxL = 9nL Add '-1nxL' to each side of the equation. -1ln + -1lnx + nxL + -1nxL = 9nL + -1nxL Combine like terms: nxL + -1nxL = 0 -1ln + -1lnx + 0 = 9nL + -1nxL -1ln + -1lnx = 9nL + -1nxL Reorder the terms: -1ln + -1lnx + -9nL + nxL = 9nL + -9nL + -1nxL + nxL Combine like terms: 9nL + -9nL = 0 -1ln + -1lnx + -9nL + nxL = 0 + -1nxL + nxL -1ln + -1lnx + -9nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -1ln + -1lnx + -9nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-1l + -1lx + -9L + 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 '(-1l + -1lx + -9L + xL)' equal to zero and attempt to solve: Simplifying -1l + -1lx + -9L + xL = 0 Reorder the terms: -9L + -1l + -1lx + xL = 0 Solving -9L + -1l + -1lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '9L' to each side of the equation. -9L + -1l + -1lx + 9L + xL = 0 + 9L Reorder the terms: -9L + 9L + -1l + -1lx + xL = 0 + 9L Combine like terms: -9L + 9L = 0 0 + -1l + -1lx + xL = 0 + 9L -1l + -1lx + xL = 0 + 9L Remove the zero: -1l + -1lx + xL = 9L Add '-1xL' to each side of the equation. -1l + -1lx + xL + -1xL = 9L + -1xL Combine like terms: xL + -1xL = 0 -1l + -1lx + 0 = 9L + -1xL -1l + -1lx = 9L + -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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