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Simplifying Log(x) + Log(x + 1) = log(20) Multiply goL * x goxL + Log(x + 1) = log(20) Reorder the terms: goxL + goL(1 + x) = log(20) goxL + (1 * goL + x * goL) = log(20) goxL + (1goL + goxL) = log(20) Reorder the terms: 1goL + goxL + goxL = log(20) Combine like terms: goxL + goxL = 2goxL 1goL + 2goxL = log(20) Reorder the terms for easier multiplication: 1goL + 2goxL = 20glo Solving 1goL + 2goxL = 20glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-20glo' to each side of the equation. 1goL + -20glo + 2goxL = 20glo + -20glo Reorder the terms: -20glo + 1goL + 2goxL = 20glo + -20glo Combine like terms: 20glo + -20glo = 0 -20glo + 1goL + 2goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-20l + L + 2xL) = 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 '(-20l + L + 2xL)' equal to zero and attempt to solve: Simplifying -20l + L + 2xL = 0 Reorder the terms: L + -20l + 2xL = 0 Solving L + -20l + 2xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-1L' to each side of the equation. L + -20l + -1L + 2xL = 0 + -1L Reorder the terms: L + -1L + -20l + 2xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -20l + 2xL = 0 + -1L -20l + 2xL = 0 + -1L Remove the zero: -20l + 2xL = -1L Add '20l' to each side of the equation. -20l + 20l + 2xL = -1L + 20l Combine like terms: -20l + 20l = 0 0 + 2xL = -1L + 20l 2xL = -1L + 20l Add '-2xL' to each side of the equation. 2xL + -2xL = -1L + 20l + -2xL Combine like terms: 2xL + -2xL = 0 0 = -1L + 20l + -2xL Simplifying 0 = -1L + 20l + -2xL 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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