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Simplifying 2logx + log(x + 5) = log(4x2 + 6x) Reorder the terms: 2glox + glo(5 + x) = log(4x2 + 6x) 2glox + (5 * glo + x * glo) = log(4x2 + 6x) 2glox + (5glo + glox) = log(4x2 + 6x) Reorder the terms: 5glo + 2glox + glox = log(4x2 + 6x) Combine like terms: 2glox + glox = 3glox 5glo + 3glox = log(4x2 + 6x) Reorder the terms: 5glo + 3glox = glo(6x + 4x2) 5glo + 3glox = (6x * glo + 4x2 * glo) 5glo + 3glox = (6glox + 4glox2) Solving 5glo + 3glox = 6glox + 4glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glox' to each side of the equation. 5glo + 3glox + -6glox = 6glox + -6glox + 4glox2 Combine like terms: 3glox + -6glox = -3glox 5glo + -3glox = 6glox + -6glox + 4glox2 Combine like terms: 6glox + -6glox = 0 5glo + -3glox = 0 + 4glox2 5glo + -3glox = 4glox2 Add '-4glox2' to each side of the equation. 5glo + -3glox + -4glox2 = 4glox2 + -4glox2 Combine like terms: 4glox2 + -4glox2 = 0 5glo + -3glox + -4glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(5 + -3x + -4x2) = 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 + -3x + -4x2)' equal to zero and attempt to solve: Simplifying 5 + -3x + -4x2 = 0 Solving 5 + -3x + -4x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -3x + -5 + -4x2 = 0 + -5 Reorder the terms: 5 + -5 + -3x + -4x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x + -4x2 = 0 + -5 -3x + -4x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3x + -4x2 = -5 Add '3x' to each side of the equation. -3x + 3x + -4x2 = -5 + 3x Combine like terms: -3x + 3x = 0 0 + -4x2 = -5 + 3x -4x2 = -5 + 3x Add '4x2' to each side of the equation. -4x2 + 4x2 = -5 + 3x + 4x2 Combine like terms: -4x2 + 4x2 = 0 0 = -5 + 3x + 4x2 Simplifying 0 = -5 + 3x + 4x2 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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