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Simplifying lnx + ln(x + 4) = ln(x2 + 12) Reorder the terms: lnx + ln(4 + x) = ln(x2 + 12) lnx + (4 * ln + x * ln) = ln(x2 + 12) lnx + (4ln + lnx) = ln(x2 + 12) Reorder the terms: 4ln + lnx + lnx = ln(x2 + 12) Combine like terms: lnx + lnx = 2lnx 4ln + 2lnx = ln(x2 + 12) Reorder the terms: 4ln + 2lnx = ln(12 + x2) 4ln + 2lnx = (12 * ln + x2 * ln) 4ln + 2lnx = (12ln + lnx2) Solving 4ln + 2lnx = 12ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. 4ln + -12ln + 2lnx = 12ln + -12ln + lnx2 Combine like terms: 4ln + -12ln = -8ln -8ln + 2lnx = 12ln + -12ln + lnx2 Combine like terms: 12ln + -12ln = 0 -8ln + 2lnx = 0 + lnx2 -8ln + 2lnx = lnx2 Add '-1lnx2' to each side of the equation. -8ln + 2lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -8ln + 2lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 2x + -1x2) = 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 '(-8 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -8 + 2x + -1x2 = 0 Solving -8 + 2x + -1x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 2x + 8 + -1x2 = 0 + 8 Reorder the terms: -8 + 8 + 2x + -1x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2x + -1x2 = 0 + 8 2x + -1x2 = 0 + 8 Combine like terms: 0 + 8 = 8 2x + -1x2 = 8 Add '-2x' to each side of the equation. 2x + -2x + -1x2 = 8 + -2x Combine like terms: 2x + -2x = 0 0 + -1x2 = 8 + -2x -1x2 = 8 + -2x Add 'x2' to each side of the equation. -1x2 + x2 = 8 + -2x + x2 Combine like terms: -1x2 + x2 = 0 0 = 8 + -2x + x2 Simplifying 0 = 8 + -2x + x2 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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