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Simplifying log(2y + -1) = log(5y + 4) Reorder the terms: glo(-1 + 2y) = log(5y + 4) (-1 * glo + 2y * glo) = log(5y + 4) (-1glo + 2gloy) = log(5y + 4) Reorder the terms: -1glo + 2gloy = glo(4 + 5y) -1glo + 2gloy = (4 * glo + 5y * glo) -1glo + 2gloy = (4glo + 5gloy) Solving -1glo + 2gloy = 4glo + 5gloy 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. -1glo + -4glo + 2gloy = 4glo + -4glo + 5gloy Combine like terms: -1glo + -4glo = -5glo -5glo + 2gloy = 4glo + -4glo + 5gloy Combine like terms: 4glo + -4glo = 0 -5glo + 2gloy = 0 + 5gloy -5glo + 2gloy = 5gloy Add '-5gloy' to each side of the equation. -5glo + 2gloy + -5gloy = 5gloy + -5gloy Combine like terms: 2gloy + -5gloy = -3gloy -5glo + -3gloy = 5gloy + -5gloy Combine like terms: 5gloy + -5gloy = 0 -5glo + -3gloy = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(5 + 3y) = 0 Ignore the factor -1.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 '(5 + 3y)' equal to zero and attempt to solve: Simplifying 5 + 3y = 0 Solving 5 + 3y = 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 + 3y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3y = 0 + -5 3y = 0 + -5 Combine like terms: 0 + -5 = -5 3y = -5 Add '-3y' to each side of the equation. 3y + -3y = -5 + -3y Combine like terms: 3y + -3y = 0 0 = -5 + -3y Simplifying 0 = -5 + -3y 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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