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