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Simplifying Log(12) = log(3x + 81) Reorder the terms for easier multiplication: 12goL = log(3x + 81) Reorder the terms: 12goL = glo(81 + 3x) 12goL = (81 * glo + 3x * glo) 12goL = (81glo + 3glox) Solving 12goL = 81glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-81glo' to each side of the equation. -81glo + 12goL = 81glo + -81glo + 3glox Combine like terms: 81glo + -81glo = 0 -81glo + 12goL = 0 + 3glox -81glo + 12goL = 3glox Add '-3glox' to each side of the equation. -81glo + -3glox + 12goL = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -81glo + -3glox + 12goL = 0 Factor out the Greatest Common Factor (GCF), '3go'. 3go(-27l + -1lx + 4L) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(-27l + -1lx + 4L)' equal to zero and attempt to solve: Simplifying -27l + -1lx + 4L = 0 Reorder the terms: 4L + -27l + -1lx = 0 Solving 4L + -27l + -1lx = 0 Move all terms containing g to the left, all other terms to the right. Add '-4L' to each side of the equation. 4L + -27l + -4L + -1lx = 0 + -4L Reorder the terms: 4L + -4L + -27l + -1lx = 0 + -4L Combine like terms: 4L + -4L = 0 0 + -27l + -1lx = 0 + -4L -27l + -1lx = 0 + -4L Remove the zero: -27l + -1lx = -4L Add '27l' to each side of the equation. -27l + 27l + -1lx = -4L + 27l Combine like terms: -27l + 27l = 0 0 + -1lx = -4L + 27l -1lx = -4L + 27l Add 'lx' to each side of the equation. -1lx + lx = -4L + 27l + lx Combine like terms: -1lx + lx = 0 0 = -4L + 27l + lx Simplifying 0 = -4L + 27l + lx 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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