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Simplifying log(2x + 1) + log(x + 4) = log(2x2 + x + 7) Reorder the terms: glo(1 + 2x) + log(x + 4) = log(2x2 + x + 7) (1 * glo + 2x * glo) + log(x + 4) = log(2x2 + x + 7) (1glo + 2glox) + log(x + 4) = log(2x2 + x + 7) Reorder the terms: 1glo + 2glox + glo(4 + x) = log(2x2 + x + 7) 1glo + 2glox + (4 * glo + x * glo) = log(2x2 + x + 7) 1glo + 2glox + (4glo + glox) = log(2x2 + x + 7) Reorder the terms: 1glo + 4glo + 2glox + glox = log(2x2 + x + 7) Combine like terms: 1glo + 4glo = 5glo 5glo + 2glox + glox = log(2x2 + x + 7) Combine like terms: 2glox + glox = 3glox 5glo + 3glox = log(2x2 + x + 7) Reorder the terms: 5glo + 3glox = glo(7 + x + 2x2) 5glo + 3glox = (7 * glo + x * glo + 2x2 * glo) 5glo + 3glox = (7glo + glox + 2glox2) Solving 5glo + 3glox = 7glo + glox + 2glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7glo' to each side of the equation. 5glo + -7glo + 3glox = 7glo + glox + -7glo + 2glox2 Combine like terms: 5glo + -7glo = -2glo -2glo + 3glox = 7glo + glox + -7glo + 2glox2 Reorder the terms: -2glo + 3glox = 7glo + -7glo + glox + 2glox2 Combine like terms: 7glo + -7glo = 0 -2glo + 3glox = 0 + glox + 2glox2 -2glo + 3glox = glox + 2glox2 Add '-1glox' to each side of the equation. -2glo + 3glox + -1glox = glox + -1glox + 2glox2 Combine like terms: 3glox + -1glox = 2glox -2glo + 2glox = glox + -1glox + 2glox2 Combine like terms: glox + -1glox = 0 -2glo + 2glox = 0 + 2glox2 -2glo + 2glox = 2glox2 Add '-2glox2' to each side of the equation. -2glo + 2glox + -2glox2 = 2glox2 + -2glox2 Combine like terms: 2glox2 + -2glox2 = 0 -2glo + 2glox + -2glox2 = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-1 + x + -1x2) = 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 '(-1 + x + -1x2)' equal to zero and attempt to solve: Simplifying -1 + x + -1x2 = 0 Solving -1 + x + -1x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + x + 1 + -1x2 = 0 + 1 Reorder the terms: -1 + 1 + x + -1x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x + -1x2 = 0 + 1 x + -1x2 = 0 + 1 Combine like terms: 0 + 1 = 1 x + -1x2 = 1 Add '-1x' to each side of the equation. x + -1x + -1x2 = 1 + -1x Combine like terms: x + -1x = 0 0 + -1x2 = 1 + -1x -1x2 = 1 + -1x Add 'x2' to each side of the equation. -1x2 + x2 = 1 + -1x + x2 Combine like terms: -1x2 + x2 = 0 0 = 1 + -1x + x2 Simplifying 0 = 1 + -1x + x2 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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