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Simplifying Log(4k + 1) = log(3k + -1) Reorder the terms: goL(1 + 4k) = log(3k + -1) (1 * goL + 4k * goL) = log(3k + -1) Reorder the terms: (4gkoL + 1goL) = log(3k + -1) (4gkoL + 1goL) = log(3k + -1) Reorder the terms: 4gkoL + 1goL = glo(-1 + 3k) 4gkoL + 1goL = (-1 * glo + 3k * glo) Reorder the terms: 4gkoL + 1goL = (3gklo + -1glo) 4gkoL + 1goL = (3gklo + -1glo) Solving 4gkoL + 1goL = 3gklo + -1glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3gklo' to each side of the equation. 4gkoL + -3gklo + 1goL = 3gklo + -3gklo + -1glo Reorder the terms: -3gklo + 4gkoL + 1goL = 3gklo + -3gklo + -1glo Combine like terms: 3gklo + -3gklo = 0 -3gklo + 4gkoL + 1goL = 0 + -1glo -3gklo + 4gkoL + 1goL = -1glo Add 'glo' to each side of the equation. -3gklo + 4gkoL + glo + 1goL = -1glo + glo Combine like terms: -1glo + glo = 0 -3gklo + 4gkoL + glo + 1goL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-3kl + 4kL + l + L) = 0Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(-3kl + 4kL + l + L)' equal to zero and attempt to solve: Simplifying -3kl + 4kL + l + L = 0 Reorder the terms: L + 4kL + -3kl + l = 0 Solving L + 4kL + -3kl + l = 0 Move all terms containing g to the left, all other terms to the right. Add '-1L' to each side of the equation. L + 4kL + -3kl + -1L + l = 0 + -1L Reorder the terms: L + -1L + 4kL + -3kl + l = 0 + -1L Combine like terms: L + -1L = 0 0 + 4kL + -3kl + l = 0 + -1L 4kL + -3kl + l = 0 + -1L Remove the zero: 4kL + -3kl + l = -1L Add '-4kL' to each side of the equation. 4kL + -3kl + -4kL + l = -1L + -4kL Reorder the terms: 4kL + -4kL + -3kl + l = -1L + -4kL Combine like terms: 4kL + -4kL = 0 0 + -3kl + l = -1L + -4kL -3kl + l = -1L + -4kL Add '3kl' to each side of the equation. -3kl + 3kl + l = -1L + -4kL + 3kl Combine like terms: -3kl + 3kl = 0 0 + l = -1L + -4kL + 3kl l = -1L + -4kL + 3kl Add '-1l' to each side of the equation. l + -1l = -1L + -4kL + 3kl + -1l Combine like terms: l + -1l = 0 0 = -1L + -4kL + 3kl + -1l Simplifying 0 = -1L + -4kL + 3kl + -1l 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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