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Simplifying log(2) + log(3x + -4) = log(2x + 4) Reorder the terms for easier multiplication: 2glo + log(3x + -4) = log(2x + 4) Reorder the terms: 2glo + glo(-4 + 3x) = log(2x + 4) 2glo + (-4 * glo + 3x * glo) = log(2x + 4) 2glo + (-4glo + 3glox) = log(2x + 4) Combine like terms: 2glo + -4glo = -2glo -2glo + 3glox = log(2x + 4) Reorder the terms: -2glo + 3glox = glo(4 + 2x) -2glo + 3glox = (4 * glo + 2x * glo) -2glo + 3glox = (4glo + 2glox) Solving -2glo + 3glox = 4glo + 2glox 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. -2glo + -4glo + 3glox = 4glo + -4glo + 2glox Combine like terms: -2glo + -4glo = -6glo -6glo + 3glox = 4glo + -4glo + 2glox Combine like terms: 4glo + -4glo = 0 -6glo + 3glox = 0 + 2glox -6glo + 3glox = 2glox Add '-2glox' to each side of the equation. -6glo + 3glox + -2glox = 2glox + -2glox Combine like terms: 3glox + -2glox = 1glox -6glo + 1glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -6glo + 1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-6 + x) = 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -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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