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