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Simplifying Ln(x + 3) + -1ln(x) = 2ln(2) Reorder the terms: nL(3 + x) + -1ln(x) = 2ln(2) (3 * nL + x * nL) + -1ln(x) = 2ln(2) (3nL + nxL) + -1ln(x) = 2ln(2) Multiply ln * x 3nL + nxL + -1lnx = 2ln(2) Reorder the terms: -1lnx + 3nL + nxL = 2ln(2) Reorder the terms for easier multiplication: -1lnx + 3nL + nxL = 2 * 2ln Multiply 2 * 2 -1lnx + 3nL + nxL = 4ln Solving -1lnx + 3nL + nxL = 4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. -1lnx + 3nL + -4ln + nxL = 4ln + -4ln Reorder the terms: -4ln + -1lnx + 3nL + nxL = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -4ln + -1lnx + 3nL + nxL = 0 Add '-3nL' to each side of the equation. -4ln + -1lnx + 3nL + -3nL + nxL = 0 + -3nL Combine like terms: 3nL + -3nL = 0 -4ln + -1lnx + 0 + nxL = 0 + -3nL -4ln + -1lnx + nxL = 0 + -3nL Remove the zero: -4ln + -1lnx + nxL = -3nL Add '-1nxL' to each side of the equation. -4ln + -1lnx + nxL + -1nxL = -3nL + -1nxL Combine like terms: nxL + -1nxL = 0 -4ln + -1lnx + 0 = -3nL + -1nxL -4ln + -1lnx = -3nL + -1nxL Reorder the terms: -4ln + -1lnx + 3nL + nxL = -3nL + 3nL + -1nxL + nxL Combine like terms: -3nL + 3nL = 0 -4ln + -1lnx + 3nL + nxL = 0 + -1nxL + nxL -4ln + -1lnx + 3nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 -4ln + -1lnx + 3nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-4l + -1lx + 3L + xL) = 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 '(-4l + -1lx + 3L + xL)' equal to zero and attempt to solve: Simplifying -4l + -1lx + 3L + xL = 0 Reorder the terms: 3L + -4l + -1lx + xL = 0 Solving 3L + -4l + -1lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-3L' to each side of the equation. 3L + -4l + -1lx + -3L + xL = 0 + -3L Reorder the terms: 3L + -3L + -4l + -1lx + xL = 0 + -3L Combine like terms: 3L + -3L = 0 0 + -4l + -1lx + xL = 0 + -3L -4l + -1lx + xL = 0 + -3L Remove the zero: -4l + -1lx + xL = -3L Add '-1xL' to each side of the equation. -4l + -1lx + xL + -1xL = -3L + -1xL Combine like terms: xL + -1xL = 0 -4l + -1lx + 0 = -3L + -1xL -4l + -1lx = -3L + -1xL 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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