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Simplifying log(2) + log(11 + -1x2) = 2log(5 + -1x) Reorder the terms for easier multiplication: 2glo + log(11 + -1x2) = 2log(5 + -1x) 2glo + (11 * glo + -1x2 * glo) = 2log(5 + -1x) 2glo + (11glo + -1glox2) = 2log(5 + -1x) Combine like terms: 2glo + 11glo = 13glo 13glo + -1glox2 = 2log(5 + -1x) 13glo + -1glox2 = (5 * 2glo + -1x * 2glo) 13glo + -1glox2 = (10glo + -2glox) Solving 13glo + -1glox2 = 10glo + -2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10glo' to each side of the equation. 13glo + -10glo + -1glox2 = 10glo + -10glo + -2glox Combine like terms: 13glo + -10glo = 3glo 3glo + -1glox2 = 10glo + -10glo + -2glox Combine like terms: 10glo + -10glo = 0 3glo + -1glox2 = 0 + -2glox 3glo + -1glox2 = -2glox Add '2glox' to each side of the equation. 3glo + 2glox + -1glox2 = -2glox + 2glox Combine like terms: -2glox + 2glox = 0 3glo + 2glox + -1glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(3 + 2x + -1x2) = 0 Factor a trinomial. glo((3 + -1x)(1 + x)) = 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 '(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.Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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