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Simplifying 2log(x) + -1log(12 + -1x) = log(x + -2) Multiply glo * x 2glox + -1log(12 + -1x) = log(x + -2) 2glox + (12 * -1glo + -1x * -1glo) = log(x + -2) 2glox + (-12glo + 1glox) = log(x + -2) Reorder the terms: -12glo + 2glox + 1glox = log(x + -2) Combine like terms: 2glox + 1glox = 3glox -12glo + 3glox = log(x + -2) Reorder the terms: -12glo + 3glox = glo(-2 + x) -12glo + 3glox = (-2 * glo + x * glo) -12glo + 3glox = (-2glo + glox) Solving -12glo + 3glox = -2glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2glo' to each side of the equation. -12glo + 2glo + 3glox = -2glo + 2glo + glox Combine like terms: -12glo + 2glo = -10glo -10glo + 3glox = -2glo + 2glo + glox Combine like terms: -2glo + 2glo = 0 -10glo + 3glox = 0 + glox -10glo + 3glox = glox Add '-1glox' to each side of the equation. -10glo + 3glox + -1glox = glox + -1glox Combine like terms: 3glox + -1glox = 2glox -10glo + 2glox = glox + -1glox Combine like terms: glox + -1glox = 0 -10glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-5 + x) = 0 Ignore the factor 2.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 '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -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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