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