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Simplifying log(2x2 + 5x) = log(14x + 56) Reorder the terms: glo(5x + 2x2) = log(14x + 56) (5x * glo + 2x2 * glo) = log(14x + 56) (5glox + 2glox2) = log(14x + 56) Reorder the terms: 5glox + 2glox2 = glo(56 + 14x) 5glox + 2glox2 = (56 * glo + 14x * glo) 5glox + 2glox2 = (56glo + 14glox) Solving 5glox + 2glox2 = 56glo + 14glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-56glo' to each side of the equation. 5glox + -56glo + 2glox2 = 56glo + -56glo + 14glox Reorder the terms: -56glo + 5glox + 2glox2 = 56glo + -56glo + 14glox Combine like terms: 56glo + -56glo = 0 -56glo + 5glox + 2glox2 = 0 + 14glox -56glo + 5glox + 2glox2 = 14glox Add '-14glox' to each side of the equation. -56glo + 5glox + -14glox + 2glox2 = 14glox + -14glox Combine like terms: 5glox + -14glox = -9glox -56glo + -9glox + 2glox2 = 14glox + -14glox Combine like terms: 14glox + -14glox = 0 -56glo + -9glox + 2glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-56 + -9x + 2x2) = 0 Factor a trinomial. glo((-7 + -2x)(8 + -1x)) = 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 '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Add '2x' to each side of the equation. -2x + 2x = 7 + 2x Combine like terms: -2x + 2x = 0 0 = 7 + 2x Simplifying 0 = 7 + 2x 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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + x 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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