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Simplifying Ln(2x + 1) + ln(x + -3) + -2lnx = 0 Reorder the terms: nL(1 + 2x) + ln(x + -3) + -2lnx = 0 (1 * nL + 2x * nL) + ln(x + -3) + -2lnx = 0 (1nL + 2nxL) + ln(x + -3) + -2lnx = 0 Reorder the terms: 1nL + 2nxL + ln(-3 + x) + -2lnx = 0 1nL + 2nxL + (-3 * ln + x * ln) + -2lnx = 0 1nL + 2nxL + (-3ln + lnx) + -2lnx = 0 Reorder the terms: -3ln + lnx + -2lnx + 1nL + 2nxL = 0 Combine like terms: lnx + -2lnx = -1lnx -3ln + -1lnx + 1nL + 2nxL = 0 Solving -3ln + -1lnx + 1nL + 2nxL = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1nL' to each side of the equation. -3ln + -1lnx + 1nL + -1nL + 2nxL = 0 + -1nL Combine like terms: 1nL + -1nL = 0 -3ln + -1lnx + 0 + 2nxL = 0 + -1nL -3ln + -1lnx + 2nxL = 0 + -1nL Remove the zero: -3ln + -1lnx + 2nxL = -1nL Add '-2nxL' to each side of the equation. -3ln + -1lnx + 2nxL + -2nxL = -1nL + -2nxL Combine like terms: 2nxL + -2nxL = 0 -3ln + -1lnx + 0 = -1nL + -2nxL -3ln + -1lnx = -1nL + -2nxL Reorder the terms: -3ln + -1lnx + nL + 2nxL = -1nL + nL + -2nxL + 2nxL Combine like terms: -1nL + nL = 0 -3ln + -1lnx + nL + 2nxL = 0 + -2nxL + 2nxL -3ln + -1lnx + nL + 2nxL = -2nxL + 2nxL Combine like terms: -2nxL + 2nxL = 0 -3ln + -1lnx + nL + 2nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-3l + -1lx + L + 2xL) = 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 + -1lx + L + 2xL)' equal to zero and attempt to solve: Simplifying -3l + -1lx + L + 2xL = 0 Reorder the terms: L + -3l + -1lx + 2xL = 0 Solving L + -3l + -1lx + 2xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-1L' to each side of the equation. L + -3l + -1lx + -1L + 2xL = 0 + -1L Reorder the terms: L + -1L + -3l + -1lx + 2xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -3l + -1lx + 2xL = 0 + -1L -3l + -1lx + 2xL = 0 + -1L Remove the zero: -3l + -1lx + 2xL = -1L Add '-2xL' to each side of the equation. -3l + -1lx + 2xL + -2xL = -1L + -2xL Combine like terms: 2xL + -2xL = 0 -3l + -1lx + 0 = -1L + -2xL -3l + -1lx = -1L + -2xL 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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