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Simplifying Log(x + 9) + -1log(2) = log(5x + 2) Reorder the terms: goL(9 + x) + -1log(2) = log(5x + 2) (9 * goL + x * goL) + -1log(2) = log(5x + 2) (9goL + goxL) + -1log(2) = log(5x + 2) Reorder the terms for easier multiplication: 9goL + goxL + -1 * 2glo = log(5x + 2) Multiply -1 * 2 9goL + goxL + -2glo = log(5x + 2) Reorder the terms: -2glo + 9goL + goxL = log(5x + 2) Reorder the terms: -2glo + 9goL + goxL = glo(2 + 5x) -2glo + 9goL + goxL = (2 * glo + 5x * glo) -2glo + 9goL + goxL = (2glo + 5glox) Solving -2glo + 9goL + goxL = 2glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glo' to each side of the equation. -2glo + 9goL + -2glo + goxL = 2glo + -2glo + 5glox Reorder the terms: -2glo + -2glo + 9goL + goxL = 2glo + -2glo + 5glox Combine like terms: -2glo + -2glo = -4glo -4glo + 9goL + goxL = 2glo + -2glo + 5glox Combine like terms: 2glo + -2glo = 0 -4glo + 9goL + goxL = 0 + 5glox -4glo + 9goL + goxL = 5glox Add '-5glox' to each side of the equation. -4glo + 9goL + -5glox + goxL = 5glox + -5glox Reorder the terms: -4glo + -5glox + 9goL + goxL = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -4glo + -5glox + 9goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-4l + -5lx + 9L + 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 '(-4l + -5lx + 9L + xL)' equal to zero and attempt to solve: Simplifying -4l + -5lx + 9L + xL = 0 Reorder the terms: 9L + -4l + -5lx + xL = 0 Solving 9L + -4l + -5lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-9L' to each side of the equation. 9L + -4l + -5lx + -9L + xL = 0 + -9L Reorder the terms: 9L + -9L + -4l + -5lx + xL = 0 + -9L Combine like terms: 9L + -9L = 0 0 + -4l + -5lx + xL = 0 + -9L -4l + -5lx + xL = 0 + -9L Remove the zero: -4l + -5lx + xL = -9L Add '4l' to each side of the equation. -4l + -5lx + 4l + xL = -9L + 4l Reorder the terms: -4l + 4l + -5lx + xL = -9L + 4l Combine like terms: -4l + 4l = 0 0 + -5lx + xL = -9L + 4l -5lx + xL = -9L + 4l Add '5lx' to each side of the equation. -5lx + 5lx + xL = -9L + 4l + 5lx Combine like terms: -5lx + 5lx = 0 0 + xL = -9L + 4l + 5lx xL = -9L + 4l + 5lx Add '-1xL' to each side of the equation. xL + -1xL = -9L + 4l + 5lx + -1xL Combine like terms: xL + -1xL = 0 0 = -9L + 4l + 5lx + -1xL Simplifying 0 = -9L + 4l + 5lx + -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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