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Simplifying log(x) + log(x + -2) = log(120) Multiply glo * x glox + log(x + -2) = log(120) Reorder the terms: glox + glo(-2 + x) = log(120) glox + (-2 * glo + x * glo) = log(120) glox + (-2glo + glox) = log(120) Reorder the terms: -2glo + glox + glox = log(120) Combine like terms: glox + glox = 2glox -2glo + 2glox = log(120) Reorder the terms for easier multiplication: -2glo + 2glox = 120glo Solving -2glo + 2glox = 120glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-120glo' to each side of the equation. -2glo + -120glo + 2glox = 120glo + -120glo Combine like terms: -2glo + -120glo = -122glo -122glo + 2glox = 120glo + -120glo Combine like terms: 120glo + -120glo = 0 -122glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-61 + 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 '(-61 + x)' equal to zero and attempt to solve: Simplifying -61 + x = 0 Solving -61 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '61' to each side of the equation. -61 + 61 + x = 0 + 61 Combine like terms: -61 + 61 = 0 0 + x = 0 + 61 x = 0 + 61 Combine like terms: 0 + 61 = 61 x = 61 Add '-1x' to each side of the equation. x + -1x = 61 + -1x Combine like terms: x + -1x = 0 0 = 61 + -1x Simplifying 0 = 61 + -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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