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Simplifying ln(2b2 + 2b) = ln(35 + b2) Reorder the terms: ln(2b + 2b2) = ln(35 + b2) (2b * ln + 2b2 * ln) = ln(35 + b2) (2bln + 2b2ln) = ln(35 + b2) 2bln + 2b2ln = (35 * ln + b2 * ln) Reorder the terms: 2bln + 2b2ln = (b2ln + 35ln) 2bln + 2b2ln = (b2ln + 35ln) Solving 2bln + 2b2ln = b2ln + 35ln Solving for variable 'b'. Combine like terms: 2b2ln + -1b2ln = 1b2ln 2bln + 1b2ln + -35ln = b2ln + 35ln + -1b2ln + -35ln Reorder the terms: 2bln + 1b2ln + -35ln = b2ln + -1b2ln + 35ln + -35ln Combine like terms: b2ln + -1b2ln = 0 2bln + 1b2ln + -35ln = 0 + 35ln + -35ln 2bln + 1b2ln + -35ln = 35ln + -35ln Combine like terms: 35ln + -35ln = 0 2bln + 1b2ln + -35ln = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(2b + b2 + -35) = 0 Factor a trinomial. ln((b + -5)(b + 7)) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing b to the left, all other terms to the right. Add '-1ln' to each side of the equation. ln + -1ln = 0 + -1ln Remove the zero: 0 = -1ln Simplifying 0 = -1ln 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 '(b + -5)' equal to zero and attempt to solve: Simplifying b + -5 = 0 Reorder the terms: -5 + b = 0 Solving -5 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + b = 0 + 5 b = 0 + 5 Combine like terms: 0 + 5 = 5 b = 5 Simplifying b = 5Subproblem 3
Set the factor '(b + 7)' equal to zero and attempt to solve: Simplifying b + 7 = 0 Reorder the terms: 7 + b = 0 Solving 7 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + b = 0 + -7 b = 0 + -7 Combine like terms: 0 + -7 = -7 b = -7 Simplifying b = -7Solution
b = {5, -7}
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