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Simplifying ln(r + 3) = ln(5s + 2) Reorder the terms: ln(3 + r) = ln(5s + 2) (3 * ln + r * ln) = ln(5s + 2) (3ln + lnr) = ln(5s + 2) Reorder the terms: 3ln + lnr = ln(2 + 5s) 3ln + lnr = (2 * ln + 5s * ln) 3ln + lnr = (2ln + 5lns) Solving 3ln + lnr = 2ln + 5lns 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. 3ln + -2ln + lnr = 2ln + -2ln + 5lns Combine like terms: 3ln + -2ln = 1ln 1ln + lnr = 2ln + -2ln + 5lns Combine like terms: 2ln + -2ln = 0 1ln + lnr = 0 + 5lns 1ln + lnr = 5lns Add '-5lns' to each side of the equation. 1ln + lnr + -5lns = 5lns + -5lns Combine like terms: 5lns + -5lns = 0 1ln + lnr + -5lns = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + r + -5s) = 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 '(1 + r + -5s)' equal to zero and attempt to solve: Simplifying 1 + r + -5s = 0 Solving 1 + r + -5s = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + r + -1 + -5s = 0 + -1 Reorder the terms: 1 + -1 + r + -5s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + r + -5s = 0 + -1 r + -5s = 0 + -1 Combine like terms: 0 + -1 = -1 r + -5s = -1 Add '-1r' to each side of the equation. r + -1r + -5s = -1 + -1r Combine like terms: r + -1r = 0 0 + -5s = -1 + -1r -5s = -1 + -1r Add '5s' to each side of the equation. -5s + 5s = -1 + -1r + 5s Combine like terms: -5s + 5s = 0 0 = -1 + -1r + 5s Simplifying 0 = -1 + -1r + 5s 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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