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Simplifying log(9)(3 + -1x) = log(9)(5x + -15) Reorder the terms for easier multiplication: 9glo(3 + -1x) = log(9)(5x + -15) (3 * 9glo + -1x * 9glo) = log(9)(5x + -15) (27glo + -9glox) = log(9)(5x + -15) Reorder the terms: 27glo + -9glox = glo * 9(-15 + 5x) Reorder the terms for easier multiplication: 27glo + -9glox = 9glo(-15 + 5x) 27glo + -9glox = (-15 * 9glo + 5x * 9glo) 27glo + -9glox = (-135glo + 45glox) Solving 27glo + -9glox = -135glo + 45glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '135glo' to each side of the equation. 27glo + 135glo + -9glox = -135glo + 135glo + 45glox Combine like terms: 27glo + 135glo = 162glo 162glo + -9glox = -135glo + 135glo + 45glox Combine like terms: -135glo + 135glo = 0 162glo + -9glox = 0 + 45glox 162glo + -9glox = 45glox Add '-45glox' to each side of the equation. 162glo + -9glox + -45glox = 45glox + -45glox Combine like terms: -9glox + -45glox = -54glox 162glo + -54glox = 45glox + -45glox Combine like terms: 45glox + -45glox = 0 162glo + -54glox = 0 Factor out the Greatest Common Factor (GCF), '54glo'. 54glo(3 + -1x) = 0 Ignore the factor 54.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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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