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Simplifying Log(7)(4r + -4) = log(7)(3r + -1) Reorder the terms: goL * 7(-4 + 4r) = log(7)(3r + -1) Reorder the terms for easier multiplication: 7goL(-4 + 4r) = log(7)(3r + -1) (-4 * 7goL + 4r * 7goL) = log(7)(3r + -1) (-28goL + 28gorL) = log(7)(3r + -1) Reorder the terms: -28goL + 28gorL = glo * 7(-1 + 3r) Reorder the terms for easier multiplication: -28goL + 28gorL = 7glo(-1 + 3r) -28goL + 28gorL = (-1 * 7glo + 3r * 7glo) -28goL + 28gorL = (-7glo + 21glor) Solving -28goL + 28gorL = -7glo + 21glor Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '7glo' to each side of the equation. -28goL + 7glo + 28gorL = -7glo + 7glo + 21glor Reorder the terms: 7glo + -28goL + 28gorL = -7glo + 7glo + 21glor Combine like terms: -7glo + 7glo = 0 7glo + -28goL + 28gorL = 0 + 21glor 7glo + -28goL + 28gorL = 21glor Add '-21glor' to each side of the equation. 7glo + -28goL + -21glor + 28gorL = 21glor + -21glor Reorder the terms: 7glo + -21glor + -28goL + 28gorL = 21glor + -21glor Combine like terms: 21glor + -21glor = 0 7glo + -21glor + -28goL + 28gorL = 0 Factor out the Greatest Common Factor (GCF), '7go'. 7go(l + -3lr + -4L + 4rL) = 0 Ignore the factor 7.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 '(l + -3lr + -4L + 4rL)' equal to zero and attempt to solve: Simplifying l + -3lr + -4L + 4rL = 0 Reorder the terms: -4L + l + -3lr + 4rL = 0 Solving -4L + l + -3lr + 4rL = 0 Move all terms containing g to the left, all other terms to the right. Add '4L' to each side of the equation. -4L + l + -3lr + 4L + 4rL = 0 + 4L Reorder the terms: -4L + 4L + l + -3lr + 4rL = 0 + 4L Combine like terms: -4L + 4L = 0 0 + l + -3lr + 4rL = 0 + 4L l + -3lr + 4rL = 0 + 4L Remove the zero: l + -3lr + 4rL = 4L Add '-1l' to each side of the equation. l + -3lr + -1l + 4rL = 4L + -1l Reorder the terms: l + -1l + -3lr + 4rL = 4L + -1l Combine like terms: l + -1l = 0 0 + -3lr + 4rL = 4L + -1l -3lr + 4rL = 4L + -1l Add '3lr' to each side of the equation. -3lr + 3lr + 4rL = 4L + -1l + 3lr Combine like terms: -3lr + 3lr = 0 0 + 4rL = 4L + -1l + 3lr 4rL = 4L + -1l + 3lr Add '-4rL' to each side of the equation. 4rL + -4rL = 4L + -1l + 3lr + -4rL Combine like terms: 4rL + -4rL = 0 0 = 4L + -1l + 3lr + -4rL Simplifying 0 = 4L + -1l + 3lr + -4rL 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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