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Simplifying Log(x + -1) + log(x + 4) + -1log(3) = log(x) Reorder the terms: goL(-1 + x) + log(x + 4) + -1log(3) = log(x) (-1 * goL + x * goL) + log(x + 4) + -1log(3) = log(x) (-1goL + goxL) + log(x + 4) + -1log(3) = log(x) Reorder the terms: -1goL + goxL + glo(4 + x) + -1log(3) = log(x) -1goL + goxL + (4 * glo + x * glo) + -1log(3) = log(x) -1goL + goxL + (4glo + glox) + -1log(3) = log(x) Reorder the terms for easier multiplication: -1goL + goxL + 4glo + glox + -1 * 3glo = log(x) Multiply -1 * 3 -1goL + goxL + 4glo + glox + -3glo = log(x) Reorder the terms: 4glo + -3glo + glox + -1goL + goxL = log(x) Combine like terms: 4glo + -3glo = 1glo 1glo + glox + -1goL + goxL = log(x) Multiply glo * x 1glo + glox + -1goL + goxL = glox Add '-1glox' to each side of the equation. 1glo + glox + -1goL + -1glox + goxL = glox + -1glox Reorder the terms: 1glo + glox + -1glox + -1goL + goxL = glox + -1glox Combine like terms: glox + -1glox = 0 1glo + 0 + -1goL + goxL = glox + -1glox 1glo + -1goL + goxL = glox + -1glox Combine like terms: glox + -1glox = 0 1glo + -1goL + goxL = 0 Solving 1glo + -1goL + goxL = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'go'. go(l + -1L + xL) = 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 '(l + -1L + xL)' equal to zero and attempt to solve: Simplifying l + -1L + xL = 0 Reorder the terms: -1L + l + xL = 0 Solving -1L + l + xL = 0 Move all terms containing g to the left, all other terms to the right. Add 'L' to each side of the equation. -1L + l + L + xL = 0 + L Reorder the terms: -1L + L + l + xL = 0 + L Combine like terms: -1L + L = 0 0 + l + xL = 0 + L l + xL = 0 + L Remove the zero: l + xL = L Add '-1l' to each side of the equation. l + -1l + xL = L + -1l Combine like terms: l + -1l = 0 0 + xL = L + -1l xL = L + -1l Add '-1xL' to each side of the equation. xL + -1xL = L + -1l + -1xL Combine like terms: xL + -1xL = 0 0 = L + -1l + -1xL Simplifying 0 = L + -1l + -1xL 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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