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Simplifying log((2x2) + -7) = 2log(x + -1) Reorder the terms: glo(-7 + (2x2)) = 2log(x + -1) (-7 * glo + (2x2) * glo) = 2log(x + -1) (-7glo + 2glox2) = 2log(x + -1) Reorder the terms: -7glo + 2glox2 = 2glo(-1 + x) -7glo + 2glox2 = (-1 * 2glo + x * 2glo) -7glo + 2glox2 = (-2glo + 2glox) Solving -7glo + 2glox2 = -2glo + 2glox 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. -7glo + 2glo + 2glox2 = -2glo + 2glo + 2glox Combine like terms: -7glo + 2glo = -5glo -5glo + 2glox2 = -2glo + 2glo + 2glox Combine like terms: -2glo + 2glo = 0 -5glo + 2glox2 = 0 + 2glox -5glo + 2glox2 = 2glox Add '-2glox' to each side of the equation. -5glo + -2glox + 2glox2 = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -5glo + -2glox + 2glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-5 + -2x + 2x2) = 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 '(-5 + -2x + 2x2)' equal to zero and attempt to solve: Simplifying -5 + -2x + 2x2 = 0 Solving -5 + -2x + 2x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -2x + 5 + 2x2 = 0 + 5 Reorder the terms: -5 + 5 + -2x + 2x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x + 2x2 = 0 + 5 -2x + 2x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2x + 2x2 = 5 Add '2x' to each side of the equation. -2x + 2x + 2x2 = 5 + 2x Combine like terms: -2x + 2x = 0 0 + 2x2 = 5 + 2x 2x2 = 5 + 2x Add '-2x2' to each side of the equation. 2x2 + -2x2 = 5 + 2x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = 5 + 2x + -2x2 Simplifying 0 = 5 + 2x + -2x2 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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