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Simplifying Log(x + -2) + log(x + 3) = log(10 + -1x) Reorder the terms: goL(-2 + x) + log(x + 3) = log(10 + -1x) (-2 * goL + x * goL) + log(x + 3) = log(10 + -1x) (-2goL + goxL) + log(x + 3) = log(10 + -1x) Reorder the terms: -2goL + goxL + glo(3 + x) = log(10 + -1x) -2goL + goxL + (3 * glo + x * glo) = log(10 + -1x) -2goL + goxL + (3glo + glox) = log(10 + -1x) Reorder the terms: 3glo + glox + -2goL + goxL = log(10 + -1x) 3glo + glox + -2goL + goxL = (10 * glo + -1x * glo) 3glo + glox + -2goL + goxL = (10glo + -1glox) Solving 3glo + glox + -2goL + goxL = 10glo + -1glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10glo' to each side of the equation. 3glo + glox + -2goL + -10glo + goxL = 10glo + -10glo + -1glox Reorder the terms: 3glo + -10glo + glox + -2goL + goxL = 10glo + -10glo + -1glox Combine like terms: 3glo + -10glo = -7glo -7glo + glox + -2goL + goxL = 10glo + -10glo + -1glox Combine like terms: 10glo + -10glo = 0 -7glo + glox + -2goL + goxL = 0 + -1glox -7glo + glox + -2goL + goxL = -1glox Add 'glox' to each side of the equation. -7glo + glox + -2goL + glox + goxL = -1glox + glox Reorder the terms: -7glo + glox + glox + -2goL + goxL = -1glox + glox Combine like terms: glox + glox = 2glox -7glo + 2glox + -2goL + goxL = -1glox + glox Combine like terms: -1glox + glox = 0 -7glo + 2glox + -2goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-7l + 2lx + -2L + 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 '(-7l + 2lx + -2L + xL)' equal to zero and attempt to solve: Simplifying -7l + 2lx + -2L + xL = 0 Reorder the terms: -2L + -7l + 2lx + xL = 0 Solving -2L + -7l + 2lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '2L' to each side of the equation. -2L + -7l + 2lx + 2L + xL = 0 + 2L Reorder the terms: -2L + 2L + -7l + 2lx + xL = 0 + 2L Combine like terms: -2L + 2L = 0 0 + -7l + 2lx + xL = 0 + 2L -7l + 2lx + xL = 0 + 2L Remove the zero: -7l + 2lx + xL = 2L Add '7l' to each side of the equation. -7l + 2lx + 7l + xL = 2L + 7l Reorder the terms: -7l + 7l + 2lx + xL = 2L + 7l Combine like terms: -7l + 7l = 0 0 + 2lx + xL = 2L + 7l 2lx + xL = 2L + 7l Add '-2lx' to each side of the equation. 2lx + -2lx + xL = 2L + 7l + -2lx Combine like terms: 2lx + -2lx = 0 0 + xL = 2L + 7l + -2lx xL = 2L + 7l + -2lx Add '-1xL' to each side of the equation. xL + -1xL = 2L + 7l + -2lx + -1xL Combine like terms: xL + -1xL = 0 0 = 2L + 7l + -2lx + -1xL Simplifying 0 = 2L + 7l + -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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