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Simplifying ln(9r + 1) = ln(r2 + 9) Reorder the terms: ln(1 + 9r) = ln(r2 + 9) (1 * ln + 9r * ln) = ln(r2 + 9) (1ln + 9lnr) = ln(r2 + 9) Reorder the terms: 1ln + 9lnr = ln(9 + r2) 1ln + 9lnr = (9 * ln + r2 * ln) 1ln + 9lnr = (9ln + lnr2) Solving 1ln + 9lnr = 9ln + lnr2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. 1ln + -9ln + 9lnr = 9ln + -9ln + lnr2 Combine like terms: 1ln + -9ln = -8ln -8ln + 9lnr = 9ln + -9ln + lnr2 Combine like terms: 9ln + -9ln = 0 -8ln + 9lnr = 0 + lnr2 -8ln + 9lnr = lnr2 Add '-1lnr2' to each side of the equation. -8ln + 9lnr + -1lnr2 = lnr2 + -1lnr2 Combine like terms: lnr2 + -1lnr2 = 0 -8ln + 9lnr + -1lnr2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 9r + -1r2) = 0 Factor a trinomial. ln((-8 + r)(1 + -1r)) = 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 '(-8 + r)' equal to zero and attempt to solve: Simplifying -8 + r = 0 Solving -8 + r = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = 0 + 8 Combine like terms: -8 + 8 = 0 0 + r = 0 + 8 r = 0 + 8 Combine like terms: 0 + 8 = 8 r = 8 Add '-1r' to each side of the equation. r + -1r = 8 + -1r Combine like terms: r + -1r = 0 0 = 8 + -1r Simplifying 0 = 8 + -1r The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -1r)' equal to zero and attempt to solve: Simplifying 1 + -1r = 0 Solving 1 + -1r = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1r = 0 + -1 -1r = 0 + -1 Combine like terms: 0 + -1 = -1 -1r = -1 Add 'r' to each side of the equation. -1r + r = -1 + r Combine like terms: -1r + r = 0 0 = -1 + r Simplifying 0 = -1 + r 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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