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Simplifying Log(6x + 1) = log(3x + -2) Reorder the terms: goL(1 + 6x) = log(3x + -2) (1 * goL + 6x * goL) = log(3x + -2) (1goL + 6goxL) = log(3x + -2) Reorder the terms: 1goL + 6goxL = glo(-2 + 3x) 1goL + 6goxL = (-2 * glo + 3x * glo) 1goL + 6goxL = (-2glo + 3glox) Solving 1goL + 6goxL = -2glo + 3glox 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. 1goL + 2glo + 6goxL = -2glo + 2glo + 3glox Reorder the terms: 2glo + 1goL + 6goxL = -2glo + 2glo + 3glox Combine like terms: -2glo + 2glo = 0 2glo + 1goL + 6goxL = 0 + 3glox 2glo + 1goL + 6goxL = 3glox Add '-3glox' to each side of the equation. 2glo + 1goL + -3glox + 6goxL = 3glox + -3glox Reorder the terms: 2glo + -3glox + 1goL + 6goxL = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 2glo + -3glox + 1goL + 6goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(2l + -3lx + L + 6xL) = 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 '(2l + -3lx + L + 6xL)' equal to zero and attempt to solve: Simplifying 2l + -3lx + L + 6xL = 0 Reorder the terms: L + 2l + -3lx + 6xL = 0 Solving L + 2l + -3lx + 6xL = 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 + -3lx + -1L + 6xL = 0 + -1L Reorder the terms: L + -1L + 2l + -3lx + 6xL = 0 + -1L Combine like terms: L + -1L = 0 0 + 2l + -3lx + 6xL = 0 + -1L 2l + -3lx + 6xL = 0 + -1L Remove the zero: 2l + -3lx + 6xL = -1L Add '-2l' to each side of the equation. 2l + -3lx + -2l + 6xL = -1L + -2l Reorder the terms: 2l + -2l + -3lx + 6xL = -1L + -2l Combine like terms: 2l + -2l = 0 0 + -3lx + 6xL = -1L + -2l -3lx + 6xL = -1L + -2l Add '3lx' to each side of the equation. -3lx + 3lx + 6xL = -1L + -2l + 3lx Combine like terms: -3lx + 3lx = 0 0 + 6xL = -1L + -2l + 3lx 6xL = -1L + -2l + 3lx Add '-6xL' to each side of the equation. 6xL + -6xL = -1L + -2l + 3lx + -6xL Combine like terms: 6xL + -6xL = 0 0 = -1L + -2l + 3lx + -6xL Simplifying 0 = -1L + -2l + 3lx + -6xL 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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