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Simplifying log(3) * 9y = log(3)(4y + 15) Reorder the terms for easier multiplication: 3 * 9glo * y = log(3)(4y + 15) Multiply 3 * 9 27glo * y = log(3)(4y + 15) Multiply glo * y 27gloy = log(3)(4y + 15) Reorder the terms: 27gloy = glo * 3(15 + 4y) Reorder the terms for easier multiplication: 27gloy = 3glo(15 + 4y) 27gloy = (15 * 3glo + 4y * 3glo) 27gloy = (45glo + 12gloy) Solving 27gloy = 45glo + 12gloy Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-45glo' to each side of the equation. -45glo + 27gloy = 45glo + -45glo + 12gloy Combine like terms: 45glo + -45glo = 0 -45glo + 27gloy = 0 + 12gloy -45glo + 27gloy = 12gloy Add '-12gloy' to each side of the equation. -45glo + 27gloy + -12gloy = 12gloy + -12gloy Combine like terms: 27gloy + -12gloy = 15gloy -45glo + 15gloy = 12gloy + -12gloy Combine like terms: 12gloy + -12gloy = 0 -45glo + 15gloy = 0 Factor out the Greatest Common Factor (GCF), '15glo'. 15glo(-3 + y) = 0 Ignore the factor 15.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 + y)' equal to zero and attempt to solve: Simplifying -3 + y = 0 Solving -3 + y = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + y = 0 + 3 y = 0 + 3 Combine like terms: 0 + 3 = 3 y = 3 Add '-1y' to each side of the equation. y + -1y = 3 + -1y Combine like terms: y + -1y = 0 0 = 3 + -1y Simplifying 0 = 3 + -1y 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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