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