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Simplifying Log(x + 2) + Log(3 + -1x) = Log(5x + 1) Reorder the terms: goL(2 + x) + Log(3 + -1x) = Log(5x + 1) (2 * goL + x * goL) + Log(3 + -1x) = Log(5x + 1) (2goL + goxL) + Log(3 + -1x) = Log(5x + 1) 2goL + goxL + (3 * goL + -1x * goL) = Log(5x + 1) 2goL + goxL + (3goL + -1goxL) = Log(5x + 1) Reorder the terms: 2goL + 3goL + goxL + -1goxL = Log(5x + 1) Combine like terms: 2goL + 3goL = 5goL 5goL + goxL + -1goxL = Log(5x + 1) Combine like terms: goxL + -1goxL = 0 5goL + 0 = Log(5x + 1) 5goL = Log(5x + 1) Reorder the terms: 5goL = goL(1 + 5x) 5goL = (1 * goL + 5x * goL) 5goL = (1goL + 5goxL) Solving 5goL = 1goL + 5goxL 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. 5goL + -1goL = 1goL + -1goL + 5goxL Combine like terms: 5goL + -1goL = 4goL 4goL = 1goL + -1goL + 5goxL Combine like terms: 1goL + -1goL = 0 4goL = 0 + 5goxL 4goL = 5goxL Add '-5goxL' to each side of the equation. 4goL + -5goxL = 5goxL + -5goxL Combine like terms: 5goxL + -5goxL = 0 4goL + -5goxL = 0 Factor out the Greatest Common Factor (GCF), 'goL'. goL(4 + -5x) = 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 '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Add '5x' to each side of the equation. -5x + 5x = -4 + 5x Combine like terms: -5x + 5x = 0 0 = -4 + 5x Simplifying 0 = -4 + 5x 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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