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Simplifying log(2x2 + 4x) = log(11x + 30) Reorder the terms: glo(4x + 2x2) = log(11x + 30) (4x * glo + 2x2 * glo) = log(11x + 30) (4glox + 2glox2) = log(11x + 30) Reorder the terms: 4glox + 2glox2 = glo(30 + 11x) 4glox + 2glox2 = (30 * glo + 11x * glo) 4glox + 2glox2 = (30glo + 11glox) Solving 4glox + 2glox2 = 30glo + 11glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-30glo' to each side of the equation. 4glox + -30glo + 2glox2 = 30glo + -30glo + 11glox Reorder the terms: -30glo + 4glox + 2glox2 = 30glo + -30glo + 11glox Combine like terms: 30glo + -30glo = 0 -30glo + 4glox + 2glox2 = 0 + 11glox -30glo + 4glox + 2glox2 = 11glox Add '-11glox' to each side of the equation. -30glo + 4glox + -11glox + 2glox2 = 11glox + -11glox Combine like terms: 4glox + -11glox = -7glox -30glo + -7glox + 2glox2 = 11glox + -11glox Combine like terms: 11glox + -11glox = 0 -30glo + -7glox + 2glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-30 + -7x + 2x2) = 0 Factor a trinomial. glo((-5 + -2x)(6 + -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 '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Add '2x' to each side of the equation. -2x + 2x = 5 + 2x Combine like terms: -2x + 2x = 0 0 = 5 + 2x Simplifying 0 = 5 + 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + 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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