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Simplifying Log(108) = Log(x + 2) + Log(x + -1) Reorder the terms for easier multiplication: 108goL = Log(x + 2) + Log(x + -1) Reorder the terms: 108goL = goL(2 + x) + Log(x + -1) 108goL = (2 * goL + x * goL) + Log(x + -1) 108goL = (2goL + goxL) + Log(x + -1) Reorder the terms: 108goL = 2goL + goxL + goL(-1 + x) 108goL = 2goL + goxL + (-1 * goL + x * goL) 108goL = 2goL + goxL + (-1goL + goxL) Reorder the terms: 108goL = 2goL + -1goL + goxL + goxL Combine like terms: 2goL + -1goL = 1goL 108goL = 1goL + goxL + goxL Combine like terms: goxL + goxL = 2goxL 108goL = 1goL + 2goxL Solving 108goL = 1goL + 2goxL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1goL' to each side of the equation. 108goL + -1goL = 1goL + -1goL + 2goxL Combine like terms: 108goL + -1goL = 107goL 107goL = 1goL + -1goL + 2goxL Combine like terms: 1goL + -1goL = 0 107goL = 0 + 2goxL 107goL = 2goxL Add '-2goxL' to each side of the equation. 107goL + -2goxL = 2goxL + -2goxL Combine like terms: 2goxL + -2goxL = 0 107goL + -2goxL = 0 Factor out the Greatest Common Factor (GCF), 'goL'. goL(107 + -2x) = 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 '(107 + -2x)' equal to zero and attempt to solve: Simplifying 107 + -2x = 0 Solving 107 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-107' to each side of the equation. 107 + -107 + -2x = 0 + -107 Combine like terms: 107 + -107 = 0 0 + -2x = 0 + -107 -2x = 0 + -107 Combine like terms: 0 + -107 = -107 -2x = -107 Add '2x' to each side of the equation. -2x + 2x = -107 + 2x Combine like terms: -2x + 2x = 0 0 = -107 + 2x Simplifying 0 = -107 + 2x 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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