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