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Simplifying Ln(2x + 3) + ln(x + -7) + -2lnx = 0 Reorder the terms: nL(3 + 2x) + ln(x + -7) + -2lnx = 0 (3 * nL + 2x * nL) + ln(x + -7) + -2lnx = 0 (3nL + 2nxL) + ln(x + -7) + -2lnx = 0 Reorder the terms: 3nL + 2nxL + ln(-7 + x) + -2lnx = 0 3nL + 2nxL + (-7 * ln + x * ln) + -2lnx = 0 3nL + 2nxL + (-7ln + lnx) + -2lnx = 0 Reorder the terms: -7ln + lnx + -2lnx + 3nL + 2nxL = 0 Combine like terms: lnx + -2lnx = -1lnx -7ln + -1lnx + 3nL + 2nxL = 0 Solving -7ln + -1lnx + 3nL + 2nxL = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3nL' to each side of the equation. -7ln + -1lnx + 3nL + -3nL + 2nxL = 0 + -3nL Combine like terms: 3nL + -3nL = 0 -7ln + -1lnx + 0 + 2nxL = 0 + -3nL -7ln + -1lnx + 2nxL = 0 + -3nL Remove the zero: -7ln + -1lnx + 2nxL = -3nL Add '-2nxL' to each side of the equation. -7ln + -1lnx + 2nxL + -2nxL = -3nL + -2nxL Combine like terms: 2nxL + -2nxL = 0 -7ln + -1lnx + 0 = -3nL + -2nxL -7ln + -1lnx = -3nL + -2nxL Reorder the terms: -7ln + -1lnx + 3nL + 2nxL = -3nL + 3nL + -2nxL + 2nxL Combine like terms: -3nL + 3nL = 0 -7ln + -1lnx + 3nL + 2nxL = 0 + -2nxL + 2nxL -7ln + -1lnx + 3nL + 2nxL = -2nxL + 2nxL Combine like terms: -2nxL + 2nxL = 0 -7ln + -1lnx + 3nL + 2nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-7l + -1lx + 3L + 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 '(-7l + -1lx + 3L + 2xL)' equal to zero and attempt to solve: Simplifying -7l + -1lx + 3L + 2xL = 0 Reorder the terms: 3L + -7l + -1lx + 2xL = 0 Solving 3L + -7l + -1lx + 2xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-3L' to each side of the equation. 3L + -7l + -1lx + -3L + 2xL = 0 + -3L Reorder the terms: 3L + -3L + -7l + -1lx + 2xL = 0 + -3L Combine like terms: 3L + -3L = 0 0 + -7l + -1lx + 2xL = 0 + -3L -7l + -1lx + 2xL = 0 + -3L Remove the zero: -7l + -1lx + 2xL = -3L Add '-2xL' to each side of the equation. -7l + -1lx + 2xL + -2xL = -3L + -2xL Combine like terms: 2xL + -2xL = 0 -7l + -1lx + 0 = -3L + -2xL -7l + -1lx = -3L + -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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