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Simplifying Log(4 + -1x) = Log(x + 6) + 2log(x + 2) (4 * goL + -1x * goL) = Log(x + 6) + 2log(x + 2) (4goL + -1goxL) = Log(x + 6) + 2log(x + 2) Reorder the terms: 4goL + -1goxL = goL(6 + x) + 2log(x + 2) 4goL + -1goxL = (6 * goL + x * goL) + 2log(x + 2) 4goL + -1goxL = (6goL + goxL) + 2log(x + 2) Reorder the terms: 4goL + -1goxL = 6goL + goxL + 2glo(2 + x) 4goL + -1goxL = 6goL + goxL + (2 * 2glo + x * 2glo) 4goL + -1goxL = 6goL + goxL + (4glo + 2glox) Reorder the terms: 4goL + -1goxL = 4glo + 2glox + 6goL + goxL Solving 4goL + -1goxL = 4glo + 2glox + 6goL + goxL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4glo' to each side of the equation. 4goL + -4glo + -1goxL = 4glo + 2glox + 6goL + -4glo + goxL Reorder the terms: -4glo + 4goL + -1goxL = 4glo + 2glox + 6goL + -4glo + goxL Reorder the terms: -4glo + 4goL + -1goxL = 4glo + -4glo + 2glox + 6goL + goxL Combine like terms: 4glo + -4glo = 0 -4glo + 4goL + -1goxL = 0 + 2glox + 6goL + goxL -4glo + 4goL + -1goxL = 2glox + 6goL + goxL Add '-2glox' to each side of the equation. -4glo + 4goL + -2glox + -1goxL = 2glox + 6goL + -2glox + goxL Reorder the terms: -4glo + -2glox + 4goL + -1goxL = 2glox + 6goL + -2glox + goxL Reorder the terms: -4glo + -2glox + 4goL + -1goxL = 2glox + -2glox + 6goL + goxL Combine like terms: 2glox + -2glox = 0 -4glo + -2glox + 4goL + -1goxL = 0 + 6goL + goxL -4glo + -2glox + 4goL + -1goxL = 6goL + goxL Add '-6goL' to each side of the equation. -4glo + -2glox + 4goL + -6goL + -1goxL = 6goL + -6goL + goxL Combine like terms: 4goL + -6goL = -2goL -4glo + -2glox + -2goL + -1goxL = 6goL + -6goL + goxL Combine like terms: 6goL + -6goL = 0 -4glo + -2glox + -2goL + -1goxL = 0 + goxL -4glo + -2glox + -2goL + -1goxL = goxL Add '-1goxL' to each side of the equation. -4glo + -2glox + -2goL + -1goxL + -1goxL = goxL + -1goxL Combine like terms: -1goxL + -1goxL = -2goxL -4glo + -2glox + -2goL + -2goxL = goxL + -1goxL Combine like terms: goxL + -1goxL = 0 -4glo + -2glox + -2goL + -2goxL = 0 Factor out the Greatest Common Factor (GCF), '-2go'. -2go(2l + lx + L + xL) = 0 Ignore the factor -2.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 '(2l + lx + L + xL)' equal to zero and attempt to solve: Simplifying 2l + lx + L + xL = 0 Reorder the terms: L + 2l + lx + xL = 0 Solving L + 2l + lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-1L' to each side of the equation. L + 2l + lx + -1L + xL = 0 + -1L Reorder the terms: L + -1L + 2l + lx + xL = 0 + -1L Combine like terms: L + -1L = 0 0 + 2l + lx + xL = 0 + -1L 2l + lx + xL = 0 + -1L Remove the zero: 2l + lx + xL = -1L Add '-2l' to each side of the equation. 2l + lx + -2l + xL = -1L + -2l Reorder the terms: 2l + -2l + lx + xL = -1L + -2l Combine like terms: 2l + -2l = 0 0 + lx + xL = -1L + -2l lx + xL = -1L + -2l Add '-1lx' to each side of the equation. lx + -1lx + xL = -1L + -2l + -1lx Combine like terms: lx + -1lx = 0 0 + xL = -1L + -2l + -1lx xL = -1L + -2l + -1lx Add '-1xL' to each side of the equation. xL + -1xL = -1L + -2l + -1lx + -1xL Combine like terms: xL + -1xL = 0 0 = -1L + -2l + -1lx + -1xL Simplifying 0 = -1L + -2l + -1lx + -1xL 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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