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