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Simplifying log(2t + -4) = log(14t + -3) Reorder the terms: glo(-4 + 2t) = log(14t + -3) (-4 * glo + 2t * glo) = log(14t + -3) (-4glo + 2glot) = log(14t + -3) Reorder the terms: -4glo + 2glot = glo(-3 + 14t) -4glo + 2glot = (-3 * glo + 14t * glo) -4glo + 2glot = (-3glo + 14glot) Solving -4glo + 2glot = -3glo + 14glot Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3glo' to each side of the equation. -4glo + 3glo + 2glot = -3glo + 3glo + 14glot Combine like terms: -4glo + 3glo = -1glo -1glo + 2glot = -3glo + 3glo + 14glot Combine like terms: -3glo + 3glo = 0 -1glo + 2glot = 0 + 14glot -1glo + 2glot = 14glot Add '-14glot' to each side of the equation. -1glo + 2glot + -14glot = 14glot + -14glot Combine like terms: 2glot + -14glot = -12glot -1glo + -12glot = 14glot + -14glot Combine like terms: 14glot + -14glot = 0 -1glo + -12glot = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(1 + 12t) = 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 '(1 + 12t)' equal to zero and attempt to solve: Simplifying 1 + 12t = 0 Solving 1 + 12t = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 12t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 12t = 0 + -1 12t = 0 + -1 Combine like terms: 0 + -1 = -1 12t = -1 Add '-12t' to each side of the equation. 12t + -12t = -1 + -12t Combine like terms: 12t + -12t = 0 0 = -1 + -12t Simplifying 0 = -1 + -12t 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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