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Simplifying Log(x) + Log(x + -1) = Log(x + -2) Multiply goL * x goxL + Log(x + -1) = Log(x + -2) Reorder the terms: goxL + goL(-1 + x) = Log(x + -2) goxL + (-1 * goL + x * goL) = Log(x + -2) goxL + (-1goL + goxL) = Log(x + -2) Reorder the terms: -1goL + goxL + goxL = Log(x + -2) Combine like terms: goxL + goxL = 2goxL -1goL + 2goxL = Log(x + -2) Reorder the terms: -1goL + 2goxL = goL(-2 + x) -1goL + 2goxL = (-2 * goL + x * goL) -1goL + 2goxL = (-2goL + goxL) Solving -1goL + 2goxL = -2goL + goxL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2goL' to each side of the equation. -1goL + 2goL + 2goxL = -2goL + 2goL + goxL Combine like terms: -1goL + 2goL = 1goL 1goL + 2goxL = -2goL + 2goL + goxL Combine like terms: -2goL + 2goL = 0 1goL + 2goxL = 0 + goxL 1goL + 2goxL = goxL Add '-1goxL' to each side of the equation. 1goL + 2goxL + -1goxL = goxL + -1goxL Combine like terms: 2goxL + -1goxL = 1goxL 1goL + 1goxL = goxL + -1goxL Combine like terms: goxL + -1goxL = 0 1goL + 1goxL = 0 Factor out the Greatest Common Factor (GCF), 'goL'. goL(1 + x) = 0Subproblem 1
Set the factor 'goL' equal to zero and attempt to solve: Simplifying goL = 0 Solving goL = 0 Move all terms containing g to the left, all other terms to the right. Simplifying goL = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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