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