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Simplifying log(3)(3x + 2) = log(3)(4x + -6) Reorder the terms: glo * 3(2 + 3x) = log(3)(4x + -6) Reorder the terms for easier multiplication: 3glo(2 + 3x) = log(3)(4x + -6) (2 * 3glo + 3x * 3glo) = log(3)(4x + -6) (6glo + 9glox) = log(3)(4x + -6) Reorder the terms: 6glo + 9glox = glo * 3(-6 + 4x) Reorder the terms for easier multiplication: 6glo + 9glox = 3glo(-6 + 4x) 6glo + 9glox = (-6 * 3glo + 4x * 3glo) 6glo + 9glox = (-18glo + 12glox) Solving 6glo + 9glox = -18glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '18glo' to each side of the equation. 6glo + 18glo + 9glox = -18glo + 18glo + 12glox Combine like terms: 6glo + 18glo = 24glo 24glo + 9glox = -18glo + 18glo + 12glox Combine like terms: -18glo + 18glo = 0 24glo + 9glox = 0 + 12glox 24glo + 9glox = 12glox Add '-12glox' to each side of the equation. 24glo + 9glox + -12glox = 12glox + -12glox Combine like terms: 9glox + -12glox = -3glox 24glo + -3glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 24glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(8 + -1x) = 0 Ignore the factor 3.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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + 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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