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Simplifying Ln(x2 + -48) = Ln(2x) Reorder the terms: nL(-48 + x2) = Ln(2x) (-48 * nL + x2 * nL) = Ln(2x) (-48nL + nx2L) = Ln(2x) Remove parenthesis around (2x) -48nL + nx2L = nL * 2x Reorder the terms for easier multiplication: -48nL + nx2L = 2nL * x Multiply nL * x -48nL + nx2L = 2nxL Solving -48nL + nx2L = 2nxL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2nxL' to each side of the equation. -48nL + -2nxL + nx2L = 2nxL + -2nxL Combine like terms: 2nxL + -2nxL = 0 -48nL + -2nxL + nx2L = 0 Factor out the Greatest Common Factor (GCF), 'nL'. nL(-48 + -2x + x2) = 0 Factor a trinomial. nL((-6 + -1x)(8 + -1x)) = 0Subproblem 1
Set the factor 'nL' equal to zero and attempt to solve: Simplifying nL = 0 Solving nL = 0 Move all terms containing n to the left, all other terms to the right. Simplifying nL = 0 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 '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Add 'x' to each side of the equation. -1x + x = 6 + x Combine like terms: -1x + x = 0 0 = 6 + x Simplifying 0 = 6 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + x 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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