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