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Simplifying Log(x + 14) + -1log(x + 6) = logx Reorder the terms: goL(14 + x) + -1log(x + 6) = logx (14 * goL + x * goL) + -1log(x + 6) = logx (14goL + goxL) + -1log(x + 6) = logx Reorder the terms: 14goL + goxL + -1glo(6 + x) = logx 14goL + goxL + (6 * -1glo + x * -1glo) = logx 14goL + goxL + (-6glo + -1glox) = logx Reorder the terms: -6glo + -1glox + 14goL + goxL = logx Solving -6glo + -1glox + 14goL + 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. -6glo + -1glox + 14goL + -1glox + goxL = glox + -1glox Reorder the terms: -6glo + -1glox + -1glox + 14goL + goxL = glox + -1glox Combine like terms: -1glox + -1glox = -2glox -6glo + -2glox + 14goL + goxL = glox + -1glox Combine like terms: glox + -1glox = 0 -6glo + -2glox + 14goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-6l + -2lx + 14L + 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 '(-6l + -2lx + 14L + xL)' equal to zero and attempt to solve: Simplifying -6l + -2lx + 14L + xL = 0 Reorder the terms: 14L + -6l + -2lx + xL = 0 Solving 14L + -6l + -2lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-14L' to each side of the equation. 14L + -6l + -2lx + -14L + xL = 0 + -14L Reorder the terms: 14L + -14L + -6l + -2lx + xL = 0 + -14L Combine like terms: 14L + -14L = 0 0 + -6l + -2lx + xL = 0 + -14L -6l + -2lx + xL = 0 + -14L Remove the zero: -6l + -2lx + xL = -14L Add '6l' to each side of the equation. -6l + -2lx + 6l + xL = -14L + 6l Reorder the terms: -6l + 6l + -2lx + xL = -14L + 6l Combine like terms: -6l + 6l = 0 0 + -2lx + xL = -14L + 6l -2lx + xL = -14L + 6l Add '2lx' to each side of the equation. -2lx + 2lx + xL = -14L + 6l + 2lx Combine like terms: -2lx + 2lx = 0 0 + xL = -14L + 6l + 2lx xL = -14L + 6l + 2lx Add '-1xL' to each side of the equation. xL + -1xL = -14L + 6l + 2lx + -1xL Combine like terms: xL + -1xL = 0 0 = -14L + 6l + 2lx + -1xL Simplifying 0 = -14L + 6l + 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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