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Simplifying Log(x + -3) + log(x + -2) = 2logx Reorder the terms: goL(-3 + x) + log(x + -2) = 2logx (-3 * goL + x * goL) + log(x + -2) = 2logx (-3goL + goxL) + log(x + -2) = 2logx Reorder the terms: -3goL + goxL + glo(-2 + x) = 2logx -3goL + goxL + (-2 * glo + x * glo) = 2logx -3goL + goxL + (-2glo + glox) = 2logx Reorder the terms: -2glo + glox + -3goL + goxL = 2logx Solving -2glo + glox + -3goL + goxL = 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glox' to each side of the equation. -2glo + glox + -3goL + -2glox + goxL = 2glox + -2glox Reorder the terms: -2glo + glox + -2glox + -3goL + goxL = 2glox + -2glox Combine like terms: glox + -2glox = -1glox -2glo + -1glox + -3goL + goxL = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -2glo + -1glox + -3goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-2l + -1lx + -3L + 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 '(-2l + -1lx + -3L + xL)' equal to zero and attempt to solve: Simplifying -2l + -1lx + -3L + xL = 0 Reorder the terms: -3L + -2l + -1lx + xL = 0 Solving -3L + -2l + -1lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '3L' to each side of the equation. -3L + -2l + -1lx + 3L + xL = 0 + 3L Reorder the terms: -3L + 3L + -2l + -1lx + xL = 0 + 3L Combine like terms: -3L + 3L = 0 0 + -2l + -1lx + xL = 0 + 3L -2l + -1lx + xL = 0 + 3L Remove the zero: -2l + -1lx + xL = 3L Add '2l' to each side of the equation. -2l + -1lx + 2l + xL = 3L + 2l Reorder the terms: -2l + 2l + -1lx + xL = 3L + 2l Combine like terms: -2l + 2l = 0 0 + -1lx + xL = 3L + 2l -1lx + xL = 3L + 2l Add 'lx' to each side of the equation. -1lx + lx + xL = 3L + 2l + lx Combine like terms: -1lx + lx = 0 0 + xL = 3L + 2l + lx xL = 3L + 2l + lx Add '-1xL' to each side of the equation. xL + -1xL = 3L + 2l + lx + -1xL Combine like terms: xL + -1xL = 0 0 = 3L + 2l + lx + -1xL Simplifying 0 = 3L + 2l + 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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