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