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Simplifying ln(x + 4) + ln(x + 3) = ln(x + -13) Reorder the terms: ln(4 + x) + ln(x + 3) = ln(x + -13) (4 * ln + x * ln) + ln(x + 3) = ln(x + -13) (4ln + lnx) + ln(x + 3) = ln(x + -13) Reorder the terms: 4ln + lnx + ln(3 + x) = ln(x + -13) 4ln + lnx + (3 * ln + x * ln) = ln(x + -13) 4ln + lnx + (3ln + lnx) = ln(x + -13) Reorder the terms: 4ln + 3ln + lnx + lnx = ln(x + -13) Combine like terms: 4ln + 3ln = 7ln 7ln + lnx + lnx = ln(x + -13) Combine like terms: lnx + lnx = 2lnx 7ln + 2lnx = ln(x + -13) Reorder the terms: 7ln + 2lnx = ln(-13 + x) 7ln + 2lnx = (-13 * ln + x * ln) 7ln + 2lnx = (-13ln + lnx) Solving 7ln + 2lnx = -13ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '13ln' to each side of the equation. 7ln + 13ln + 2lnx = -13ln + 13ln + lnx Combine like terms: 7ln + 13ln = 20ln 20ln + 2lnx = -13ln + 13ln + lnx Combine like terms: -13ln + 13ln = 0 20ln + 2lnx = 0 + lnx 20ln + 2lnx = lnx Add '-1lnx' to each side of the equation. 20ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx 20ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 20ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(20 + 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 '(20 + x)' equal to zero and attempt to solve: Simplifying 20 + x = 0 Solving 20 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + x = 0 + -20 x = 0 + -20 Combine like terms: 0 + -20 = -20 x = -20 Add '-1x' to each side of the equation. x + -1x = -20 + -1x Combine like terms: x + -1x = 0 0 = -20 + -1x Simplifying 0 = -20 + -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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