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Simplifying log(2x + 5) = log(5x + -4) Reorder the terms: glo(5 + 2x) = log(5x + -4) (5 * glo + 2x * glo) = log(5x + -4) (5glo + 2glox) = log(5x + -4) Reorder the terms: 5glo + 2glox = glo(-4 + 5x) 5glo + 2glox = (-4 * glo + 5x * glo) 5glo + 2glox = (-4glo + 5glox) Solving 5glo + 2glox = -4glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '4glo' to each side of the equation. 5glo + 4glo + 2glox = -4glo + 4glo + 5glox Combine like terms: 5glo + 4glo = 9glo 9glo + 2glox = -4glo + 4glo + 5glox Combine like terms: -4glo + 4glo = 0 9glo + 2glox = 0 + 5glox 9glo + 2glox = 5glox Add '-5glox' to each side of the equation. 9glo + 2glox + -5glox = 5glox + -5glox Combine like terms: 2glox + -5glox = -3glox 9glo + -3glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 9glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(3 + -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 '(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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