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Simplifying 2log(x) = log(-6 + 5x) Multiply glo * x 2glox = log(-6 + 5x) 2glox = (-6 * glo + 5x * glo) 2glox = (-6glo + 5glox) Solving 2glox = -6glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '6glo' to each side of the equation. 6glo + 2glox = -6glo + 6glo + 5glox Combine like terms: -6glo + 6glo = 0 6glo + 2glox = 0 + 5glox 6glo + 2glox = 5glox Add '-5glox' to each side of the equation. 6glo + 2glox + -5glox = 5glox + -5glox Combine like terms: 2glox + -5glox = -3glox 6glo + -3glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 6glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(2 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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