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Simplifying 2log(x) = log(2) + log(6x + -10) Multiply glo * x 2glox = log(2) + log(6x + -10) Reorder the terms for easier multiplication: 2glox = 2glo + log(6x + -10) Reorder the terms: 2glox = 2glo + glo(-10 + 6x) 2glox = 2glo + (-10 * glo + 6x * glo) 2glox = 2glo + (-10glo + 6glox) Combine like terms: 2glo + -10glo = -8glo 2glox = -8glo + 6glox Solving 2glox = -8glo + 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '8glo' to each side of the equation. 8glo + 2glox = -8glo + 8glo + 6glox Combine like terms: -8glo + 8glo = 0 8glo + 2glox = 0 + 6glox 8glo + 2glox = 6glox Add '-6glox' to each side of the equation. 8glo + 2glox + -6glox = 6glox + -6glox Combine like terms: 2glox + -6glox = -4glox 8glo + -4glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 8glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(2 + -1x) = 0 Ignore the factor 4.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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