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Simplifying log(2t + 4) = log(14 + -3t) Reorder the terms: glo(4 + 2t) = log(14 + -3t) (4 * glo + 2t * glo) = log(14 + -3t) (4glo + 2glot) = log(14 + -3t) 4glo + 2glot = (14 * glo + -3t * glo) 4glo + 2glot = (14glo + -3glot) Solving 4glo + 2glot = 14glo + -3glot Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-14glo' to each side of the equation. 4glo + -14glo + 2glot = 14glo + -14glo + -3glot Combine like terms: 4glo + -14glo = -10glo -10glo + 2glot = 14glo + -14glo + -3glot Combine like terms: 14glo + -14glo = 0 -10glo + 2glot = 0 + -3glot -10glo + 2glot = -3glot Add '3glot' to each side of the equation. -10glo + 2glot + 3glot = -3glot + 3glot Combine like terms: 2glot + 3glot = 5glot -10glo + 5glot = -3glot + 3glot Combine like terms: -3glot + 3glot = 0 -10glo + 5glot = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-2 + t) = 0 Ignore the factor 5.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 + t)' equal to zero and attempt to solve: Simplifying -2 + t = 0 Solving -2 + t = 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 + t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + t = 0 + 2 t = 0 + 2 Combine like terms: 0 + 2 = 2 t = 2 Add '-1t' to each side of the equation. t + -1t = 2 + -1t Combine like terms: t + -1t = 0 0 = 2 + -1t Simplifying 0 = 2 + -1t 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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