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Simplifying Log(x + 2) + log(x + -3) = log(3 + -14) Reorder the terms: goL(2 + x) + log(x + -3) = log(3 + -14) (2 * goL + x * goL) + log(x + -3) = log(3 + -14) (2goL + goxL) + log(x + -3) = log(3 + -14) Reorder the terms: 2goL + goxL + glo(-3 + x) = log(3 + -14) 2goL + goxL + (-3 * glo + x * glo) = log(3 + -14) 2goL + goxL + (-3glo + glox) = log(3 + -14) Reorder the terms: -3glo + glox + 2goL + goxL = log(3 + -14) Combine like terms: 3 + -14 = -11 -3glo + glox + 2goL + goxL = glo(-11) Reorder the terms for easier multiplication: -3glo + glox + 2goL + goxL = -11glo Solving -3glo + glox + 2goL + goxL = -11glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '11glo' to each side of the equation. -3glo + glox + 2goL + 11glo + goxL = -11glo + 11glo Reorder the terms: -3glo + 11glo + glox + 2goL + goxL = -11glo + 11glo Combine like terms: -3glo + 11glo = 8glo 8glo + glox + 2goL + goxL = -11glo + 11glo Combine like terms: -11glo + 11glo = 0 8glo + glox + 2goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(8l + lx + 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 '(8l + lx + 2L + xL)' equal to zero and attempt to solve: Simplifying 8l + lx + 2L + xL = 0 Reorder the terms: 2L + 8l + lx + xL = 0 Solving 2L + 8l + lx + 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 + 8l + lx + -2L + xL = 0 + -2L Reorder the terms: 2L + -2L + 8l + lx + xL = 0 + -2L Combine like terms: 2L + -2L = 0 0 + 8l + lx + xL = 0 + -2L 8l + lx + xL = 0 + -2L Remove the zero: 8l + lx + xL = -2L Add '-8l' to each side of the equation. 8l + lx + -8l + xL = -2L + -8l Reorder the terms: 8l + -8l + lx + xL = -2L + -8l Combine like terms: 8l + -8l = 0 0 + lx + xL = -2L + -8l lx + xL = -2L + -8l Add '-1lx' to each side of the equation. lx + -1lx + xL = -2L + -8l + -1lx Combine like terms: lx + -1lx = 0 0 + xL = -2L + -8l + -1lx xL = -2L + -8l + -1lx Add '-1xL' to each side of the equation. xL + -1xL = -2L + -8l + -1lx + -1xL Combine like terms: xL + -1xL = 0 0 = -2L + -8l + -1lx + -1xL Simplifying 0 = -2L + -8l + -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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