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Simplifying ln(x2 + 3x) + -1ln(x) = 0 Reorder the terms: ln(3x + x2) + -1ln(x) = 0 (3x * ln + x2 * ln) + -1ln(x) = 0 (3lnx + lnx2) + -1ln(x) = 0 Multiply ln * x 3lnx + lnx2 + -1lnx = 0 Reorder the terms: 3lnx + -1lnx + lnx2 = 0 Combine like terms: 3lnx + -1lnx = 2lnx 2lnx + lnx2 = 0 Solving 2lnx + lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'lnx'. lnx(2 + x) = 0Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve: Simplifying lnx = 0 Solving lnx = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx = 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -1x 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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