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Simplifying log(3)(5x + 3) = log(3)(3x + 9) Reorder the terms: glo * 3(3 + 5x) = log(3)(3x + 9) Reorder the terms for easier multiplication: 3glo(3 + 5x) = log(3)(3x + 9) (3 * 3glo + 5x * 3glo) = log(3)(3x + 9) (9glo + 15glox) = log(3)(3x + 9) Reorder the terms: 9glo + 15glox = glo * 3(9 + 3x) Reorder the terms for easier multiplication: 9glo + 15glox = 3glo(9 + 3x) 9glo + 15glox = (9 * 3glo + 3x * 3glo) 9glo + 15glox = (27glo + 9glox) Solving 9glo + 15glox = 27glo + 9glox 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. 9glo + -27glo + 15glox = 27glo + -27glo + 9glox Combine like terms: 9glo + -27glo = -18glo -18glo + 15glox = 27glo + -27glo + 9glox Combine like terms: 27glo + -27glo = 0 -18glo + 15glox = 0 + 9glox -18glo + 15glox = 9glox Add '-9glox' to each side of the equation. -18glo + 15glox + -9glox = 9glox + -9glox Combine like terms: 15glox + -9glox = 6glox -18glo + 6glox = 9glox + -9glox Combine like terms: 9glox + -9glox = 0 -18glo + 6glox = 0 Factor out the Greatest Common Factor (GCF), '6glo'. 6glo(-3 + x) = 0 Ignore the factor 6.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 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x 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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