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Simplifying Log(x + 1) + log(x + 3) = log(8) Reorder the terms: goL(1 + x) + log(x + 3) = log(8) (1 * goL + x * goL) + log(x + 3) = log(8) (1goL + goxL) + log(x + 3) = log(8) Reorder the terms: 1goL + goxL + glo(3 + x) = log(8) 1goL + goxL + (3 * glo + x * glo) = log(8) 1goL + goxL + (3glo + glox) = log(8) Reorder the terms: 3glo + glox + 1goL + goxL = log(8) Reorder the terms for easier multiplication: 3glo + glox + 1goL + goxL = 8glo Solving 3glo + glox + 1goL + goxL = 8glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8glo' to each side of the equation. 3glo + glox + 1goL + -8glo + goxL = 8glo + -8glo Reorder the terms: 3glo + -8glo + glox + 1goL + goxL = 8glo + -8glo Combine like terms: 3glo + -8glo = -5glo -5glo + glox + 1goL + goxL = 8glo + -8glo Combine like terms: 8glo + -8glo = 0 -5glo + glox + 1goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-5l + lx + L + 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 '(-5l + lx + L + xL)' equal to zero and attempt to solve: Simplifying -5l + lx + L + xL = 0 Reorder the terms: L + -5l + lx + xL = 0 Solving L + -5l + lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-1L' to each side of the equation. L + -5l + lx + -1L + xL = 0 + -1L Reorder the terms: L + -1L + -5l + lx + xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -5l + lx + xL = 0 + -1L -5l + lx + xL = 0 + -1L Remove the zero: -5l + lx + xL = -1L Add '5l' to each side of the equation. -5l + lx + 5l + xL = -1L + 5l Reorder the terms: -5l + 5l + lx + xL = -1L + 5l Combine like terms: -5l + 5l = 0 0 + lx + xL = -1L + 5l lx + xL = -1L + 5l Add '-1lx' to each side of the equation. lx + -1lx + xL = -1L + 5l + -1lx Combine like terms: lx + -1lx = 0 0 + xL = -1L + 5l + -1lx xL = -1L + 5l + -1lx Add '-1xL' to each side of the equation. xL + -1xL = -1L + 5l + -1lx + -1xL Combine like terms: xL + -1xL = 0 0 = -1L + 5l + -1lx + -1xL Simplifying 0 = -1L + 5l + -1lx + -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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