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Simplifying ln(x + 5) + ln(x + 8) = ln(7) Reorder the terms: ln(5 + x) + ln(x + 8) = ln(7) (5 * ln + x * ln) + ln(x + 8) = ln(7) (5ln + lnx) + ln(x + 8) = ln(7) Reorder the terms: 5ln + lnx + ln(8 + x) = ln(7) 5ln + lnx + (8 * ln + x * ln) = ln(7) 5ln + lnx + (8ln + lnx) = ln(7) Reorder the terms: 5ln + 8ln + lnx + lnx = ln(7) Combine like terms: 5ln + 8ln = 13ln 13ln + lnx + lnx = ln(7) Combine like terms: lnx + lnx = 2lnx 13ln + 2lnx = ln(7) Reorder the terms for easier multiplication: 13ln + 2lnx = 7ln Solving 13ln + 2lnx = 7ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. 13ln + -7ln + 2lnx = 7ln + -7ln Combine like terms: 13ln + -7ln = 6ln 6ln + 2lnx = 7ln + -7ln Combine like terms: 7ln + -7ln = 0 6ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(3 + x) = 0 Ignore the factor 2.Subproblem 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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