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