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Simplifying Log(x + 2) + Log(x + -1) = Log(54) Reorder the terms: goL(2 + x) + Log(x + -1) = Log(54) (2 * goL + x * goL) + Log(x + -1) = Log(54) (2goL + goxL) + Log(x + -1) = Log(54) Reorder the terms: 2goL + goxL + goL(-1 + x) = Log(54) 2goL + goxL + (-1 * goL + x * goL) = Log(54) 2goL + goxL + (-1goL + goxL) = Log(54) Reorder the terms: 2goL + -1goL + goxL + goxL = Log(54) Combine like terms: 2goL + -1goL = 1goL 1goL + goxL + goxL = Log(54) Combine like terms: goxL + goxL = 2goxL 1goL + 2goxL = Log(54) Reorder the terms for easier multiplication: 1goL + 2goxL = 54goL Solving 1goL + 2goxL = 54goL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-54goL' to each side of the equation. 1goL + -54goL + 2goxL = 54goL + -54goL Combine like terms: 1goL + -54goL = -53goL -53goL + 2goxL = 54goL + -54goL Combine like terms: 54goL + -54goL = 0 -53goL + 2goxL = 0 Factor out the Greatest Common Factor (GCF), 'goL'. goL(-53 + 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 '(-53 + 2x)' equal to zero and attempt to solve: Simplifying -53 + 2x = 0 Solving -53 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + 2x = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 2x = 0 + 53 2x = 0 + 53 Combine like terms: 0 + 53 = 53 2x = 53 Add '-2x' to each side of the equation. 2x + -2x = 53 + -2x Combine like terms: 2x + -2x = 0 0 = 53 + -2x Simplifying 0 = 53 + -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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