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Simplifying ln(x2 + x + 1) * x + x4 = 0 Reorder the terms: ln(1 + x + x2) * x + x4 = 0 Reorder the terms for easier multiplication: ln * x(1 + x + x2) + x4 = 0 Multiply ln * x lnx(1 + x + x2) + x4 = 0 (1 * lnx + x * lnx + x2 * lnx) + x4 = 0 (1lnx + lnx2 + lnx3) + x4 = 0 Solving 1lnx + lnx2 + lnx3 + x4 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1x4' to each side of the equation. 1lnx + lnx2 + lnx3 + x4 + -1x4 = 0 + -1x4 Combine like terms: x4 + -1x4 = 0 1lnx + lnx2 + lnx3 + 0 = 0 + -1x4 1lnx + lnx2 + lnx3 = 0 + -1x4 Remove the zero: 1lnx + lnx2 + lnx3 = -1x4 Combine like terms: -1x4 + x4 = 0 1lnx + lnx2 + lnx3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(ln + lnx + lnx2 + x3) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(ln + lnx + lnx2 + x3)' equal to zero and attempt to solve: Simplifying ln + lnx + lnx2 + x3 = 0 Solving ln + lnx + lnx2 + x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-1x3' to each side of the equation. ln + lnx + lnx2 + x3 + -1x3 = 0 + -1x3 Combine like terms: x3 + -1x3 = 0 ln + lnx + lnx2 + 0 = 0 + -1x3 ln + lnx + lnx2 = 0 + -1x3 Remove the zero: ln + lnx + lnx2 = -1x3 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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