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Simplifying Ln(3x + -5) + -1ln(2x + 1) = 0 Reorder the terms: nL(-5 + 3x) + -1ln(2x + 1) = 0 (-5 * nL + 3x * nL) + -1ln(2x + 1) = 0 (-5nL + 3nxL) + -1ln(2x + 1) = 0 Reorder the terms: -5nL + 3nxL + -1ln(1 + 2x) = 0 -5nL + 3nxL + (1 * -1ln + 2x * -1ln) = 0 -5nL + 3nxL + (-1ln + -2lnx) = 0 Reorder the terms: -1ln + -2lnx + -5nL + 3nxL = 0 Solving -1ln + -2lnx + -5nL + 3nxL = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5nL' to each side of the equation. -1ln + -2lnx + -5nL + 5nL + 3nxL = 0 + 5nL Combine like terms: -5nL + 5nL = 0 -1ln + -2lnx + 0 + 3nxL = 0 + 5nL -1ln + -2lnx + 3nxL = 0 + 5nL Remove the zero: -1ln + -2lnx + 3nxL = 5nL Add '-3nxL' to each side of the equation. -1ln + -2lnx + 3nxL + -3nxL = 5nL + -3nxL Combine like terms: 3nxL + -3nxL = 0 -1ln + -2lnx + 0 = 5nL + -3nxL -1ln + -2lnx = 5nL + -3nxL Reorder the terms: -1ln + -2lnx + -5nL + 3nxL = 5nL + -5nL + -3nxL + 3nxL Combine like terms: 5nL + -5nL = 0 -1ln + -2lnx + -5nL + 3nxL = 0 + -3nxL + 3nxL -1ln + -2lnx + -5nL + 3nxL = -3nxL + 3nxL Combine like terms: -3nxL + 3nxL = 0 -1ln + -2lnx + -5nL + 3nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-1l + -2lx + -5L + 3xL) = 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 '(-1l + -2lx + -5L + 3xL)' equal to zero and attempt to solve: Simplifying -1l + -2lx + -5L + 3xL = 0 Reorder the terms: -5L + -1l + -2lx + 3xL = 0 Solving -5L + -1l + -2lx + 3xL = 0 Move all terms containing l to the left, all other terms to the right. Add '5L' to each side of the equation. -5L + -1l + -2lx + 5L + 3xL = 0 + 5L Reorder the terms: -5L + 5L + -1l + -2lx + 3xL = 0 + 5L Combine like terms: -5L + 5L = 0 0 + -1l + -2lx + 3xL = 0 + 5L -1l + -2lx + 3xL = 0 + 5L Remove the zero: -1l + -2lx + 3xL = 5L Add '-3xL' to each side of the equation. -1l + -2lx + 3xL + -3xL = 5L + -3xL Combine like terms: 3xL + -3xL = 0 -1l + -2lx + 0 = 5L + -3xL -1l + -2lx = 5L + -3xL 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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