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