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Simplifying Log(x + 10) + -1log(x + 4) = logx Reorder the terms: goL(10 + x) + -1log(x + 4) = logx (10 * goL + x * goL) + -1log(x + 4) = logx (10goL + goxL) + -1log(x + 4) = logx Reorder the terms: 10goL + goxL + -1glo(4 + x) = logx 10goL + goxL + (4 * -1glo + x * -1glo) = logx 10goL + goxL + (-4glo + -1glox) = logx Reorder the terms: -4glo + -1glox + 10goL + goxL = logx Solving -4glo + -1glox + 10goL + goxL = glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glox' to each side of the equation. -4glo + -1glox + 10goL + -1glox + goxL = glox + -1glox Reorder the terms: -4glo + -1glox + -1glox + 10goL + goxL = glox + -1glox Combine like terms: -1glox + -1glox = -2glox -4glo + -2glox + 10goL + goxL = glox + -1glox Combine like terms: glox + -1glox = 0 -4glo + -2glox + 10goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-4l + -2lx + 10L + 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 + 10L + xL)' equal to zero and attempt to solve: Simplifying -4l + -2lx + 10L + xL = 0 Reorder the terms: 10L + -4l + -2lx + xL = 0 Solving 10L + -4l + -2lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-10L' to each side of the equation. 10L + -4l + -2lx + -10L + xL = 0 + -10L Reorder the terms: 10L + -10L + -4l + -2lx + xL = 0 + -10L Combine like terms: 10L + -10L = 0 0 + -4l + -2lx + xL = 0 + -10L -4l + -2lx + xL = 0 + -10L Remove the zero: -4l + -2lx + xL = -10L Add '4l' to each side of the equation. -4l + -2lx + 4l + xL = -10L + 4l Reorder the terms: -4l + 4l + -2lx + xL = -10L + 4l Combine like terms: -4l + 4l = 0 0 + -2lx + xL = -10L + 4l -2lx + xL = -10L + 4l Add '2lx' to each side of the equation. -2lx + 2lx + xL = -10L + 4l + 2lx Combine like terms: -2lx + 2lx = 0 0 + xL = -10L + 4l + 2lx xL = -10L + 4l + 2lx Add '-1xL' to each side of the equation. xL + -1xL = -10L + 4l + 2lx + -1xL Combine like terms: xL + -1xL = 0 0 = -10L + 4l + 2lx + -1xL Simplifying 0 = -10L + 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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