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Simplifying ln(x2 + 7x) = ln(x2 + x + -6) Reorder the terms: ln(7x + x2) = ln(x2 + x + -6) (7x * ln + x2 * ln) = ln(x2 + x + -6) (7lnx + lnx2) = ln(x2 + x + -6) Reorder the terms: 7lnx + lnx2 = ln(-6 + x + x2) 7lnx + lnx2 = (-6 * ln + x * ln + x2 * ln) 7lnx + lnx2 = (-6ln + lnx + lnx2) Add '-1lnx2' to each side of the equation. 7lnx + lnx2 + -1lnx2 = -6ln + lnx + lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 7lnx + 0 = -6ln + lnx + lnx2 + -1lnx2 7lnx = -6ln + lnx + lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 7lnx = -6ln + lnx + 0 7lnx = -6ln + lnx Solving 7lnx = -6ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. 6ln + 7lnx = -6ln + 6ln + lnx Combine like terms: -6ln + 6ln = 0 6ln + 7lnx = 0 + lnx 6ln + 7lnx = lnx Add '-1lnx' to each side of the equation. 6ln + 7lnx + -1lnx = lnx + -1lnx Combine like terms: 7lnx + -1lnx = 6lnx 6ln + 6lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 6ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(1 + x) = 0 Ignore the factor 6.Subproblem 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 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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