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Simplifying Log(5 + -3x) = Log(4x + -9) (5 * goL + -3x * goL) = Log(4x + -9) (5goL + -3goxL) = Log(4x + -9) Reorder the terms: 5goL + -3goxL = goL(-9 + 4x) 5goL + -3goxL = (-9 * goL + 4x * goL) 5goL + -3goxL = (-9goL + 4goxL) Solving 5goL + -3goxL = -9goL + 4goxL Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '9goL' to each side of the equation. 5goL + 9goL + -3goxL = -9goL + 9goL + 4goxL Combine like terms: 5goL + 9goL = 14goL 14goL + -3goxL = -9goL + 9goL + 4goxL Combine like terms: -9goL + 9goL = 0 14goL + -3goxL = 0 + 4goxL 14goL + -3goxL = 4goxL Add '-4goxL' to each side of the equation. 14goL + -3goxL + -4goxL = 4goxL + -4goxL Combine like terms: -3goxL + -4goxL = -7goxL 14goL + -7goxL = 4goxL + -4goxL Combine like terms: 4goxL + -4goxL = 0 14goL + -7goxL = 0 Factor out the Greatest Common Factor (GCF), '7goL'. 7goL(2 + -1x) = 0 Ignore the factor 7.Subproblem 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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