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Simplifying ln(x + 6) + -1ln(x + -3) = ln(x) Reorder the terms: ln(6 + x) + -1ln(x + -3) = ln(x) (6 * ln + x * ln) + -1ln(x + -3) = ln(x) (6ln + lnx) + -1ln(x + -3) = ln(x) Reorder the terms: 6ln + lnx + -1ln(-3 + x) = ln(x) 6ln + lnx + (-3 * -1ln + x * -1ln) = ln(x) 6ln + lnx + (3ln + -1lnx) = ln(x) Reorder the terms: 6ln + 3ln + lnx + -1lnx = ln(x) Combine like terms: 6ln + 3ln = 9ln 9ln + lnx + -1lnx = ln(x) Combine like terms: lnx + -1lnx = 0 9ln + 0 = ln(x) 9ln = ln(x) Multiply ln * x 9ln = lnx Solving 9ln = 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. 9ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 9ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + -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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Add 'x' to each side of the equation. -1x + x = -9 + x Combine like terms: -1x + x = 0 0 = -9 + x Simplifying 0 = -9 + 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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