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Simplifying Log(x + -2) = log(4x + 1) + -1log(x + 2) Reorder the terms: goL(-2 + x) = log(4x + 1) + -1log(x + 2) (-2 * goL + x * goL) = log(4x + 1) + -1log(x + 2) (-2goL + goxL) = log(4x + 1) + -1log(x + 2) Reorder the terms: -2goL + goxL = glo(1 + 4x) + -1log(x + 2) -2goL + goxL = (1 * glo + 4x * glo) + -1log(x + 2) -2goL + goxL = (1glo + 4glox) + -1log(x + 2) Reorder the terms: -2goL + goxL = 1glo + 4glox + -1glo(2 + x) -2goL + goxL = 1glo + 4glox + (2 * -1glo + x * -1glo) -2goL + goxL = 1glo + 4glox + (-2glo + -1glox) Reorder the terms: -2goL + goxL = 1glo + -2glo + 4glox + -1glox Combine like terms: 1glo + -2glo = -1glo -2goL + goxL = -1glo + 4glox + -1glox Combine like terms: 4glox + -1glox = 3glox -2goL + goxL = -1glo + 3glox Solving -2goL + goxL = -1glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add 'glo' to each side of the equation. -2goL + glo + goxL = -1glo + glo + 3glox Reorder the terms: glo + -2goL + goxL = -1glo + glo + 3glox Combine like terms: -1glo + glo = 0 glo + -2goL + goxL = 0 + 3glox glo + -2goL + goxL = 3glox Add '-3glox' to each side of the equation. glo + -2goL + -3glox + goxL = 3glox + -3glox Reorder the terms: glo + -3glox + -2goL + goxL = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 glo + -3glox + -2goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(l + -3lx + -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 '(l + -3lx + -2L + xL)' equal to zero and attempt to solve: Simplifying l + -3lx + -2L + xL = 0 Reorder the terms: -2L + l + -3lx + xL = 0 Solving -2L + l + -3lx + 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 + l + -3lx + 2L + xL = 0 + 2L Reorder the terms: -2L + 2L + l + -3lx + xL = 0 + 2L Combine like terms: -2L + 2L = 0 0 + l + -3lx + xL = 0 + 2L l + -3lx + xL = 0 + 2L Remove the zero: l + -3lx + xL = 2L Add '-1l' to each side of the equation. l + -3lx + -1l + xL = 2L + -1l Reorder the terms: l + -1l + -3lx + xL = 2L + -1l Combine like terms: l + -1l = 0 0 + -3lx + xL = 2L + -1l -3lx + xL = 2L + -1l Add '3lx' to each side of the equation. -3lx + 3lx + xL = 2L + -1l + 3lx Combine like terms: -3lx + 3lx = 0 0 + xL = 2L + -1l + 3lx xL = 2L + -1l + 3lx Add '-1xL' to each side of the equation. xL + -1xL = 2L + -1l + 3lx + -1xL Combine like terms: xL + -1xL = 0 0 = 2L + -1l + 3lx + -1xL Simplifying 0 = 2L + -1l + 3lx + -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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