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Simplifying Ln(x + 9) + ln(x + -5) = 2lnx Reorder the terms: nL(9 + x) + ln(x + -5) = 2lnx (9 * nL + x * nL) + ln(x + -5) = 2lnx (9nL + nxL) + ln(x + -5) = 2lnx Reorder the terms: 9nL + nxL + ln(-5 + x) = 2lnx 9nL + nxL + (-5 * ln + x * ln) = 2lnx 9nL + nxL + (-5ln + lnx) = 2lnx Reorder the terms: -5ln + lnx + 9nL + nxL = 2lnx Solving -5ln + lnx + 9nL + 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. -5ln + lnx + 9nL + -2lnx + nxL = 2lnx + -2lnx Reorder the terms: -5ln + lnx + -2lnx + 9nL + nxL = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -5ln + -1lnx + 9nL + nxL = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -5ln + -1lnx + 9nL + nxL = 0 Add '-9nL' to each side of the equation. -5ln + -1lnx + 9nL + -9nL + nxL = 0 + -9nL Combine like terms: 9nL + -9nL = 0 -5ln + -1lnx + 0 + nxL = 0 + -9nL -5ln + -1lnx + nxL = 0 + -9nL Remove the zero: -5ln + -1lnx + nxL = -9nL Add '-1nxL' to each side of the equation. -5ln + -1lnx + nxL + -1nxL = -9nL + -1nxL Combine like terms: nxL + -1nxL = 0 -5ln + -1lnx + 0 = -9nL + -1nxL -5ln + -1lnx = -9nL + -1nxL Reorder the terms: -5ln + -1lnx + 9nL + nxL = -9nL + 9nL + -1nxL + nxL Combine like terms: -9nL + 9nL = 0 -5ln + -1lnx + 9nL + nxL = 0 + -1nxL + nxL -5ln + -1lnx + 9nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -5ln + -1lnx + 9nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-5l + -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 '(-5l + -1lx + 9L + xL)' equal to zero and attempt to solve: Simplifying -5l + -1lx + 9L + xL = 0 Reorder the terms: 9L + -5l + -1lx + xL = 0 Solving 9L + -5l + -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 + -5l + -1lx + -9L + xL = 0 + -9L Reorder the terms: 9L + -9L + -5l + -1lx + xL = 0 + -9L Combine like terms: 9L + -9L = 0 0 + -5l + -1lx + xL = 0 + -9L -5l + -1lx + xL = 0 + -9L Remove the zero: -5l + -1lx + xL = -9L Add '-1xL' to each side of the equation. -5l + -1lx + xL + -1xL = -9L + -1xL Combine like terms: xL + -1xL = 0 -5l + -1lx + 0 = -9L + -1xL -5l + -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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