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Simplifying log(2x + -5) = log(4 + -1x) Reorder the terms: glo(-5 + 2x) = log(4 + -1x) (-5 * glo + 2x * glo) = log(4 + -1x) (-5glo + 2glox) = log(4 + -1x) -5glo + 2glox = (4 * glo + -1x * glo) -5glo + 2glox = (4glo + -1glox) Solving -5glo + 2glox = 4glo + -1glox 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. -5glo + -4glo + 2glox = 4glo + -4glo + -1glox Combine like terms: -5glo + -4glo = -9glo -9glo + 2glox = 4glo + -4glo + -1glox Combine like terms: 4glo + -4glo = 0 -9glo + 2glox = 0 + -1glox -9glo + 2glox = -1glox Add 'glox' to each side of the equation. -9glo + 2glox + glox = -1glox + glox Combine like terms: 2glox + glox = 3glox -9glo + 3glox = -1glox + glox Combine like terms: -1glox + glox = 0 -9glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-3 + x) = 0 Ignore the factor 3.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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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