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