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Simplifying Log(2x + -1) = log(4x + -3) + -1logx Reorder the terms: goL(-1 + 2x) = log(4x + -3) + -1logx (-1 * goL + 2x * goL) = log(4x + -3) + -1logx (-1goL + 2goxL) = log(4x + -3) + -1logx Reorder the terms: -1goL + 2goxL = glo(-3 + 4x) + -1logx -1goL + 2goxL = (-3 * glo + 4x * glo) + -1logx -1goL + 2goxL = (-3glo + 4glox) + -1logx Combine like terms: 4glox + -1glox = 3glox -1goL + 2goxL = -3glo + 3glox Solving -1goL + 2goxL = -3glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3glo' to each side of the equation. -1goL + 3glo + 2goxL = -3glo + 3glo + 3glox Reorder the terms: 3glo + -1goL + 2goxL = -3glo + 3glo + 3glox Combine like terms: -3glo + 3glo = 0 3glo + -1goL + 2goxL = 0 + 3glox 3glo + -1goL + 2goxL = 3glox Add '-3glox' to each side of the equation. 3glo + -1goL + -3glox + 2goxL = 3glox + -3glox Reorder the terms: 3glo + -3glox + -1goL + 2goxL = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 3glo + -3glox + -1goL + 2goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(3l + -3lx + -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 '(3l + -3lx + -1L + 2xL)' equal to zero and attempt to solve: Simplifying 3l + -3lx + -1L + 2xL = 0 Reorder the terms: -1L + 3l + -3lx + 2xL = 0 Solving -1L + 3l + -3lx + 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 + 3l + -3lx + L + 2xL = 0 + L Reorder the terms: -1L + L + 3l + -3lx + 2xL = 0 + L Combine like terms: -1L + L = 0 0 + 3l + -3lx + 2xL = 0 + L 3l + -3lx + 2xL = 0 + L Remove the zero: 3l + -3lx + 2xL = L Add '-3l' to each side of the equation. 3l + -3lx + -3l + 2xL = L + -3l Reorder the terms: 3l + -3l + -3lx + 2xL = L + -3l Combine like terms: 3l + -3l = 0 0 + -3lx + 2xL = L + -3l -3lx + 2xL = L + -3l Add '3lx' to each side of the equation. -3lx + 3lx + 2xL = L + -3l + 3lx Combine like terms: -3lx + 3lx = 0 0 + 2xL = L + -3l + 3lx 2xL = L + -3l + 3lx Add '-2xL' to each side of the equation. 2xL + -2xL = L + -3l + 3lx + -2xL Combine like terms: 2xL + -2xL = 0 0 = L + -3l + 3lx + -2xL Simplifying 0 = L + -3l + 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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