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Simplifying ln(x + 5) = ln(x + -7) + -1ln(x + 7) Reorder the terms: ln(5 + x) = ln(x + -7) + -1ln(x + 7) (5 * ln + x * ln) = ln(x + -7) + -1ln(x + 7) (5ln + lnx) = ln(x + -7) + -1ln(x + 7) Reorder the terms: 5ln + lnx = ln(-7 + x) + -1ln(x + 7) 5ln + lnx = (-7 * ln + x * ln) + -1ln(x + 7) 5ln + lnx = (-7ln + lnx) + -1ln(x + 7) Reorder the terms: 5ln + lnx = -7ln + lnx + -1ln(7 + x) 5ln + lnx = -7ln + lnx + (7 * -1ln + x * -1ln) 5ln + lnx = -7ln + lnx + (-7ln + -1lnx) Reorder the terms: 5ln + lnx = -7ln + -7ln + lnx + -1lnx Combine like terms: -7ln + -7ln = -14ln 5ln + lnx = -14ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 5ln + lnx = -14ln + 0 5ln + lnx = -14ln Solving 5ln + lnx = -14ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '14ln' to each side of the equation. 5ln + 14ln + lnx = -14ln + 14ln Combine like terms: 5ln + 14ln = 19ln 19ln + lnx = -14ln + 14ln Combine like terms: -14ln + 14ln = 0 19ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(19 + 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 '(19 + x)' equal to zero and attempt to solve: Simplifying 19 + x = 0 Solving 19 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + x = 0 + -19 x = 0 + -19 Combine like terms: 0 + -19 = -19 x = -19 Add '-1x' to each side of the equation. x + -1x = -19 + -1x Combine like terms: x + -1x = 0 0 = -19 + -1x Simplifying 0 = -19 + -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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