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Simplifying ln(x + 7) = ln(x + 1) + -1ln(x + 3) Reorder the terms: ln(7 + x) = ln(x + 1) + -1ln(x + 3) (7 * ln + x * ln) = ln(x + 1) + -1ln(x + 3) (7ln + lnx) = ln(x + 1) + -1ln(x + 3) Reorder the terms: 7ln + lnx = ln(1 + x) + -1ln(x + 3) 7ln + lnx = (1 * ln + x * ln) + -1ln(x + 3) 7ln + lnx = (1ln + lnx) + -1ln(x + 3) Reorder the terms: 7ln + lnx = 1ln + lnx + -1ln(3 + x) 7ln + lnx = 1ln + lnx + (3 * -1ln + x * -1ln) 7ln + lnx = 1ln + lnx + (-3ln + -1lnx) Reorder the terms: 7ln + lnx = 1ln + -3ln + lnx + -1lnx Combine like terms: 1ln + -3ln = -2ln 7ln + lnx = -2ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 7ln + lnx = -2ln + 0 7ln + lnx = -2ln Solving 7ln + lnx = -2ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 7ln + 2ln + lnx = -2ln + 2ln Combine like terms: 7ln + 2ln = 9ln 9ln + lnx = -2ln + 2ln Combine like terms: -2ln + 2ln = 0 9ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Add '-1x' to each side of the equation. x + -1x = -9 + -1x Combine like terms: x + -1x = 0 0 = -9 + -1x Simplifying 0 = -9 + -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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