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Simplifying Log(x) + log(x + -4) = log(3x) Multiply goL * x goxL + log(x + -4) = log(3x) Reorder the terms: goxL + glo(-4 + x) = log(3x) goxL + (-4 * glo + x * glo) = log(3x) goxL + (-4glo + glox) = log(3x) Reorder the terms: -4glo + glox + goxL = log(3x) Remove parenthesis around (3x) -4glo + glox + goxL = glo * 3x Reorder the terms for easier multiplication: -4glo + glox + goxL = 3glo * x Multiply glo * x -4glo + glox + goxL = 3glox Solving -4glo + glox + goxL = 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glox' to each side of the equation. -4glo + glox + -3glox + goxL = 3glox + -3glox Combine like terms: glox + -3glox = -2glox -4glo + -2glox + goxL = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -4glo + -2glox + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-4l + -2lx + 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 '(-4l + -2lx + xL)' equal to zero and attempt to solve: Simplifying -4l + -2lx + xL = 0 Solving -4l + -2lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '4l' to each side of the equation. -4l + -2lx + 4l + xL = 0 + 4l Reorder the terms: -4l + 4l + -2lx + xL = 0 + 4l Combine like terms: -4l + 4l = 0 0 + -2lx + xL = 0 + 4l -2lx + xL = 0 + 4l Remove the zero: -2lx + xL = 4l Add '2lx' to each side of the equation. -2lx + 2lx + xL = 4l + 2lx Combine like terms: -2lx + 2lx = 0 0 + xL = 4l + 2lx xL = 4l + 2lx Add '-1xL' to each side of the equation. xL + -1xL = 4l + 2lx + -1xL Combine like terms: xL + -1xL = 0 0 = 4l + 2lx + -1xL Simplifying 0 = 4l + 2lx + -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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