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Simplifying Log(x + 8) + -1log(x + 7) = log(3) Reorder the terms: goL(8 + x) + -1log(x + 7) = log(3) (8 * goL + x * goL) + -1log(x + 7) = log(3) (8goL + goxL) + -1log(x + 7) = log(3) Reorder the terms: 8goL + goxL + -1glo(7 + x) = log(3) 8goL + goxL + (7 * -1glo + x * -1glo) = log(3) 8goL + goxL + (-7glo + -1glox) = log(3) Reorder the terms: -7glo + -1glox + 8goL + goxL = log(3) Reorder the terms for easier multiplication: -7glo + -1glox + 8goL + goxL = 3glo Solving -7glo + -1glox + 8goL + goxL = 3glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glo' to each side of the equation. -7glo + -1glox + 8goL + -3glo + goxL = 3glo + -3glo Reorder the terms: -7glo + -3glo + -1glox + 8goL + goxL = 3glo + -3glo Combine like terms: -7glo + -3glo = -10glo -10glo + -1glox + 8goL + goxL = 3glo + -3glo Combine like terms: 3glo + -3glo = 0 -10glo + -1glox + 8goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-10l + -1lx + 8L + 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 '(-10l + -1lx + 8L + xL)' equal to zero and attempt to solve: Simplifying -10l + -1lx + 8L + xL = 0 Reorder the terms: 8L + -10l + -1lx + xL = 0 Solving 8L + -10l + -1lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-8L' to each side of the equation. 8L + -10l + -1lx + -8L + xL = 0 + -8L Reorder the terms: 8L + -8L + -10l + -1lx + xL = 0 + -8L Combine like terms: 8L + -8L = 0 0 + -10l + -1lx + xL = 0 + -8L -10l + -1lx + xL = 0 + -8L Remove the zero: -10l + -1lx + xL = -8L Add '10l' to each side of the equation. -10l + -1lx + 10l + xL = -8L + 10l Reorder the terms: -10l + 10l + -1lx + xL = -8L + 10l Combine like terms: -10l + 10l = 0 0 + -1lx + xL = -8L + 10l -1lx + xL = -8L + 10l Add 'lx' to each side of the equation. -1lx + lx + xL = -8L + 10l + lx Combine like terms: -1lx + lx = 0 0 + xL = -8L + 10l + lx xL = -8L + 10l + lx Add '-1xL' to each side of the equation. xL + -1xL = -8L + 10l + lx + -1xL Combine like terms: xL + -1xL = 0 0 = -8L + 10l + lx + -1xL Simplifying 0 = -8L + 10l + lx + -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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