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Simplifying ln(x2 + 5x + 4) = ln(x + 4) Reorder the terms: ln(4 + 5x + x2) = ln(x + 4) (4 * ln + 5x * ln + x2 * ln) = ln(x + 4) (4ln + 5lnx + lnx2) = ln(x + 4) Reorder the terms: 4ln + 5lnx + lnx2 = ln(4 + x) 4ln + 5lnx + lnx2 = (4 * ln + x * ln) 4ln + 5lnx + lnx2 = (4ln + lnx) Add '-4ln' to each side of the equation. 4ln + 5lnx + -4ln + lnx2 = 4ln + -4ln + lnx Reorder the terms: 4ln + -4ln + 5lnx + lnx2 = 4ln + -4ln + lnx Combine like terms: 4ln + -4ln = 0 0 + 5lnx + lnx2 = 4ln + -4ln + lnx 5lnx + lnx2 = 4ln + -4ln + lnx Combine like terms: 4ln + -4ln = 0 5lnx + lnx2 = 0 + lnx 5lnx + lnx2 = lnx Solving 5lnx + lnx2 = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. 5lnx + -1lnx + lnx2 = lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx 4lnx + lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 4lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'lnx'. lnx(4 + 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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