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Simplifying Log(x + -1) + -1log(2x + -1) = log(x2 + 5) Reorder the terms: goL(-1 + x) + -1log(2x + -1) = log(x2 + 5) (-1 * goL + x * goL) + -1log(2x + -1) = log(x2 + 5) (-1goL + goxL) + -1log(2x + -1) = log(x2 + 5) Reorder the terms: -1goL + goxL + -1glo(-1 + 2x) = log(x2 + 5) -1goL + goxL + (-1 * -1glo + 2x * -1glo) = log(x2 + 5) -1goL + goxL + (1glo + -2glox) = log(x2 + 5) Reorder the terms: 1glo + -2glox + -1goL + goxL = log(x2 + 5) Reorder the terms: 1glo + -2glox + -1goL + goxL = glo(5 + x2) 1glo + -2glox + -1goL + goxL = (5 * glo + x2 * glo) 1glo + -2glox + -1goL + goxL = (5glo + glox2) Solving 1glo + -2glox + -1goL + goxL = 5glo + glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glo' to each side of the equation. 1glo + -2glox + -1goL + -5glo + goxL = 5glo + -5glo + glox2 Reorder the terms: 1glo + -5glo + -2glox + -1goL + goxL = 5glo + -5glo + glox2 Combine like terms: 1glo + -5glo = -4glo -4glo + -2glox + -1goL + goxL = 5glo + -5glo + glox2 Combine like terms: 5glo + -5glo = 0 -4glo + -2glox + -1goL + goxL = 0 + glox2 -4glo + -2glox + -1goL + goxL = glox2 Add '-1glox2' to each side of the equation. -4glo + -2glox + -1goL + -1glox2 + goxL = glox2 + -1glox2 Reorder the terms: -4glo + -2glox + -1glox2 + -1goL + goxL = glox2 + -1glox2 Combine like terms: glox2 + -1glox2 = 0 -4glo + -2glox + -1glox2 + -1goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-4l + -2lx + -1lx2 + -1L + xL) = 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 '(-4l + -2lx + -1lx2 + -1L + xL)' equal to zero and attempt to solve: Simplifying -4l + -2lx + -1lx2 + -1L + xL = 0 Reorder the terms: -1L + -4l + -2lx + -1lx2 + xL = 0 Solving -1L + -4l + -2lx + -1lx2 + xL = 0 Move all terms containing g to the left, all other terms to the right. Add 'L' to each side of the equation. -1L + -4l + -2lx + -1lx2 + L + xL = 0 + L Reorder the terms: -1L + L + -4l + -2lx + -1lx2 + xL = 0 + L Combine like terms: -1L + L = 0 0 + -4l + -2lx + -1lx2 + xL = 0 + L -4l + -2lx + -1lx2 + xL = 0 + L Remove the zero: -4l + -2lx + -1lx2 + xL = L Add '4l' to each side of the equation. -4l + -2lx + -1lx2 + 4l + xL = L + 4l Reorder the terms: -4l + 4l + -2lx + -1lx2 + xL = L + 4l Combine like terms: -4l + 4l = 0 0 + -2lx + -1lx2 + xL = L + 4l -2lx + -1lx2 + xL = L + 4l Add '2lx' to each side of the equation. -2lx + -1lx2 + 2lx + xL = L + 4l + 2lx Reorder the terms: -2lx + 2lx + -1lx2 + xL = L + 4l + 2lx Combine like terms: -2lx + 2lx = 0 0 + -1lx2 + xL = L + 4l + 2lx -1lx2 + xL = L + 4l + 2lx Add 'lx2' to each side of the equation. -1lx2 + lx2 + xL = L + 4l + 2lx + lx2 Combine like terms: -1lx2 + lx2 = 0 0 + xL = L + 4l + 2lx + lx2 xL = L + 4l + 2lx + lx2 Add '-1xL' to each side of the equation. xL + -1xL = L + 4l + 2lx + lx2 + -1xL Combine like terms: xL + -1xL = 0 0 = L + 4l + 2lx + lx2 + -1xL Simplifying 0 = L + 4l + 2lx + lx2 + -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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