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