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Simplifying ln(x + 3) * lnx = ln(x + -1) Reorder the terms: ln(3 + x) * lnx = ln(x + -1) Reorder the terms for easier multiplication: ln * lnx(3 + x) = ln(x + -1) Multiply ln * lnx l2n2x(3 + x) = ln(x + -1) (3 * l2n2x + x * l2n2x) = ln(x + -1) (3l2n2x + l2n2x2) = ln(x + -1) Reorder the terms: 3l2n2x + l2n2x2 = ln(-1 + x) 3l2n2x + l2n2x2 = (-1 * ln + x * ln) 3l2n2x + l2n2x2 = (-1ln + lnx) Solving 3l2n2x + l2n2x2 = -1ln + lnx Solving for variable 'l'. Reorder the terms: ln + -1lnx + 3l2n2x + l2n2x2 = -1ln + lnx + ln + -1lnx Reorder the terms: ln + -1lnx + 3l2n2x + l2n2x2 = -1ln + ln + lnx + -1lnx Combine like terms: -1ln + ln = 0 ln + -1lnx + 3l2n2x + l2n2x2 = 0 + lnx + -1lnx ln + -1lnx + 3l2n2x + l2n2x2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 ln + -1lnx + 3l2n2x + l2n2x2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -1x + 3lnx + lnx2) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 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 '(1 + -1x + 3lnx + lnx2)' equal to zero and attempt to solve: Simplifying 1 + -1x + 3lnx + lnx2 = 0 Reorder the terms: 1 + 3lnx + lnx2 + -1x = 0 Solving 1 + 3lnx + lnx2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 3lnx + lnx2 + -1 + -1x = 0 + -1 Reorder the terms: 1 + -1 + 3lnx + lnx2 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3lnx + lnx2 + -1x = 0 + -1 3lnx + lnx2 + -1x = 0 + -1 Combine like terms: 0 + -1 = -1 3lnx + lnx2 + -1x = -1 Add 'x' to each side of the equation. 3lnx + lnx2 + -1x + x = -1 + x Combine like terms: -1x + x = 0 3lnx + lnx2 + 0 = -1 + x 3lnx + lnx2 = -1 + 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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