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Simplifying 2ln(r) = ln(15r + 34) Multiply ln * r 2lnr = ln(15r + 34) Reorder the terms: 2lnr = ln(34 + 15r) 2lnr = (34 * ln + 15r * ln) 2lnr = (34ln + 15lnr) Solving 2lnr = 34ln + 15lnr Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-34ln' to each side of the equation. -34ln + 2lnr = 34ln + -34ln + 15lnr Combine like terms: 34ln + -34ln = 0 -34ln + 2lnr = 0 + 15lnr -34ln + 2lnr = 15lnr Add '-15lnr' to each side of the equation. -34ln + 2lnr + -15lnr = 15lnr + -15lnr Combine like terms: 2lnr + -15lnr = -13lnr -34ln + -13lnr = 15lnr + -15lnr Combine like terms: 15lnr + -15lnr = 0 -34ln + -13lnr = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(34 + 13r) = 0 Ignore the factor -1.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 '(34 + 13r)' equal to zero and attempt to solve: Simplifying 34 + 13r = 0 Solving 34 + 13r = 0 Move all terms containing l to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + 13r = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 13r = 0 + -34 13r = 0 + -34 Combine like terms: 0 + -34 = -34 13r = -34 Add '-13r' to each side of the equation. 13r + -13r = -34 + -13r Combine like terms: 13r + -13r = 0 0 = -34 + -13r Simplifying 0 = -34 + -13r 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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