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Simplifying Log(x + -6) + log(x + 3) = log(10) Reorder the terms: goL(-6 + x) + log(x + 3) = log(10) (-6 * goL + x * goL) + log(x + 3) = log(10) (-6goL + goxL) + log(x + 3) = log(10) Reorder the terms: -6goL + goxL + glo(3 + x) = log(10) -6goL + goxL + (3 * glo + x * glo) = log(10) -6goL + goxL + (3glo + glox) = log(10) Reorder the terms: 3glo + glox + -6goL + goxL = log(10) Reorder the terms for easier multiplication: 3glo + glox + -6goL + goxL = 10glo Solving 3glo + glox + -6goL + goxL = 10glo 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 + -6goL + -10glo + goxL = 10glo + -10glo Reorder the terms: 3glo + -10glo + glox + -6goL + goxL = 10glo + -10glo Combine like terms: 3glo + -10glo = -7glo -7glo + glox + -6goL + goxL = 10glo + -10glo Combine like terms: 10glo + -10glo = 0 -7glo + glox + -6goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-7l + lx + -6L + 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 + lx + -6L + xL)' equal to zero and attempt to solve: Simplifying -7l + lx + -6L + xL = 0 Reorder the terms: -6L + -7l + lx + xL = 0 Solving -6L + -7l + lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '6L' to each side of the equation. -6L + -7l + lx + 6L + xL = 0 + 6L Reorder the terms: -6L + 6L + -7l + lx + xL = 0 + 6L Combine like terms: -6L + 6L = 0 0 + -7l + lx + xL = 0 + 6L -7l + lx + xL = 0 + 6L Remove the zero: -7l + lx + xL = 6L Add '7l' to each side of the equation. -7l + lx + 7l + xL = 6L + 7l Reorder the terms: -7l + 7l + lx + xL = 6L + 7l Combine like terms: -7l + 7l = 0 0 + lx + xL = 6L + 7l lx + xL = 6L + 7l Add '-1lx' to each side of the equation. lx + -1lx + xL = 6L + 7l + -1lx Combine like terms: lx + -1lx = 0 0 + xL = 6L + 7l + -1lx xL = 6L + 7l + -1lx Add '-1xL' to each side of the equation. xL + -1xL = 6L + 7l + -1lx + -1xL Combine like terms: xL + -1xL = 0 0 = 6L + 7l + -1lx + -1xL Simplifying 0 = 6L + 7l + -1lx + -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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