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Simplifying Log(3)(3x + -5) = log(3)(5x + -9) Reorder the terms: goL * 3(-5 + 3x) = log(3)(5x + -9) Reorder the terms for easier multiplication: 3goL(-5 + 3x) = log(3)(5x + -9) (-5 * 3goL + 3x * 3goL) = log(3)(5x + -9) (-15goL + 9goxL) = log(3)(5x + -9) Reorder the terms: -15goL + 9goxL = glo * 3(-9 + 5x) Reorder the terms for easier multiplication: -15goL + 9goxL = 3glo(-9 + 5x) -15goL + 9goxL = (-9 * 3glo + 5x * 3glo) -15goL + 9goxL = (-27glo + 15glox) Solving -15goL + 9goxL = -27glo + 15glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '27glo' to each side of the equation. -15goL + 27glo + 9goxL = -27glo + 27glo + 15glox Reorder the terms: 27glo + -15goL + 9goxL = -27glo + 27glo + 15glox Combine like terms: -27glo + 27glo = 0 27glo + -15goL + 9goxL = 0 + 15glox 27glo + -15goL + 9goxL = 15glox Add '-15glox' to each side of the equation. 27glo + -15goL + -15glox + 9goxL = 15glox + -15glox Reorder the terms: 27glo + -15glox + -15goL + 9goxL = 15glox + -15glox Combine like terms: 15glox + -15glox = 0 27glo + -15glox + -15goL + 9goxL = 0 Factor out the Greatest Common Factor (GCF), '3go'. 3go(9l + -5lx + -5L + 3xL) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(9l + -5lx + -5L + 3xL)' equal to zero and attempt to solve: Simplifying 9l + -5lx + -5L + 3xL = 0 Reorder the terms: -5L + 9l + -5lx + 3xL = 0 Solving -5L + 9l + -5lx + 3xL = 0 Move all terms containing g to the left, all other terms to the right. Add '5L' to each side of the equation. -5L + 9l + -5lx + 5L + 3xL = 0 + 5L Reorder the terms: -5L + 5L + 9l + -5lx + 3xL = 0 + 5L Combine like terms: -5L + 5L = 0 0 + 9l + -5lx + 3xL = 0 + 5L 9l + -5lx + 3xL = 0 + 5L Remove the zero: 9l + -5lx + 3xL = 5L Add '-9l' to each side of the equation. 9l + -5lx + -9l + 3xL = 5L + -9l Reorder the terms: 9l + -9l + -5lx + 3xL = 5L + -9l Combine like terms: 9l + -9l = 0 0 + -5lx + 3xL = 5L + -9l -5lx + 3xL = 5L + -9l Add '5lx' to each side of the equation. -5lx + 5lx + 3xL = 5L + -9l + 5lx Combine like terms: -5lx + 5lx = 0 0 + 3xL = 5L + -9l + 5lx 3xL = 5L + -9l + 5lx Add '-3xL' to each side of the equation. 3xL + -3xL = 5L + -9l + 5lx + -3xL Combine like terms: 3xL + -3xL = 0 0 = 5L + -9l + 5lx + -3xL Simplifying 0 = 5L + -9l + 5lx + -3xL 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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