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Simplifying log(5 + -2x) = log(3x + 3) (5 * glo + -2x * glo) = log(3x + 3) (5glo + -2glox) = log(3x + 3) Reorder the terms: 5glo + -2glox = glo(3 + 3x) 5glo + -2glox = (3 * glo + 3x * glo) 5glo + -2glox = (3glo + 3glox) Solving 5glo + -2glox = 3glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glo' to each side of the equation. 5glo + -3glo + -2glox = 3glo + -3glo + 3glox Combine like terms: 5glo + -3glo = 2glo 2glo + -2glox = 3glo + -3glo + 3glox Combine like terms: 3glo + -3glo = 0 2glo + -2glox = 0 + 3glox 2glo + -2glox = 3glox Add '-3glox' to each side of the equation. 2glo + -2glox + -3glox = 3glox + -3glox Combine like terms: -2glox + -3glox = -5glox 2glo + -5glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 2glo + -5glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(2 + -5x) = 0Subproblem 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 '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Add '5x' to each side of the equation. -5x + 5x = -2 + 5x Combine like terms: -5x + 5x = 0 0 = -2 + 5x Simplifying 0 = -2 + 5x 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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