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Simplifying Log(2x + 4) = log(3x + -12) Reorder the terms: goL(4 + 2x) = log(3x + -12) (4 * goL + 2x * goL) = log(3x + -12) (4goL + 2goxL) = log(3x + -12) Reorder the terms: 4goL + 2goxL = glo(-12 + 3x) 4goL + 2goxL = (-12 * glo + 3x * glo) 4goL + 2goxL = (-12glo + 3glox) Solving 4goL + 2goxL = -12glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '12glo' to each side of the equation. 4goL + 12glo + 2goxL = -12glo + 12glo + 3glox Reorder the terms: 12glo + 4goL + 2goxL = -12glo + 12glo + 3glox Combine like terms: -12glo + 12glo = 0 12glo + 4goL + 2goxL = 0 + 3glox 12glo + 4goL + 2goxL = 3glox Add '-3glox' to each side of the equation. 12glo + 4goL + -3glox + 2goxL = 3glox + -3glox Reorder the terms: 12glo + -3glox + 4goL + 2goxL = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 12glo + -3glox + 4goL + 2goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(12l + -3lx + 4L + 2xL) = 0Subproblem 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 '(12l + -3lx + 4L + 2xL)' equal to zero and attempt to solve: Simplifying 12l + -3lx + 4L + 2xL = 0 Reorder the terms: 4L + 12l + -3lx + 2xL = 0 Solving 4L + 12l + -3lx + 2xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-4L' to each side of the equation. 4L + 12l + -3lx + -4L + 2xL = 0 + -4L Reorder the terms: 4L + -4L + 12l + -3lx + 2xL = 0 + -4L Combine like terms: 4L + -4L = 0 0 + 12l + -3lx + 2xL = 0 + -4L 12l + -3lx + 2xL = 0 + -4L Remove the zero: 12l + -3lx + 2xL = -4L Add '-12l' to each side of the equation. 12l + -3lx + -12l + 2xL = -4L + -12l Reorder the terms: 12l + -12l + -3lx + 2xL = -4L + -12l Combine like terms: 12l + -12l = 0 0 + -3lx + 2xL = -4L + -12l -3lx + 2xL = -4L + -12l Add '3lx' to each side of the equation. -3lx + 3lx + 2xL = -4L + -12l + 3lx Combine like terms: -3lx + 3lx = 0 0 + 2xL = -4L + -12l + 3lx 2xL = -4L + -12l + 3lx Add '-2xL' to each side of the equation. 2xL + -2xL = -4L + -12l + 3lx + -2xL Combine like terms: 2xL + -2xL = 0 0 = -4L + -12l + 3lx + -2xL Simplifying 0 = -4L + -12l + 3lx + -2xL 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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