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Simplifying Log(x + 10) + -1log(2) = log(3x + 2) Reorder the terms: goL(10 + x) + -1log(2) = log(3x + 2) (10 * goL + x * goL) + -1log(2) = log(3x + 2) (10goL + goxL) + -1log(2) = log(3x + 2) Reorder the terms for easier multiplication: 10goL + goxL + -1 * 2glo = log(3x + 2) Multiply -1 * 2 10goL + goxL + -2glo = log(3x + 2) Reorder the terms: -2glo + 10goL + goxL = log(3x + 2) Reorder the terms: -2glo + 10goL + goxL = glo(2 + 3x) -2glo + 10goL + goxL = (2 * glo + 3x * glo) -2glo + 10goL + goxL = (2glo + 3glox) Solving -2glo + 10goL + goxL = 2glo + 3glox 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 + 10goL + -2glo + goxL = 2glo + -2glo + 3glox Reorder the terms: -2glo + -2glo + 10goL + goxL = 2glo + -2glo + 3glox Combine like terms: -2glo + -2glo = -4glo -4glo + 10goL + goxL = 2glo + -2glo + 3glox Combine like terms: 2glo + -2glo = 0 -4glo + 10goL + goxL = 0 + 3glox -4glo + 10goL + goxL = 3glox Add '-3glox' to each side of the equation. -4glo + 10goL + -3glox + goxL = 3glox + -3glox Reorder the terms: -4glo + -3glox + 10goL + goxL = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -4glo + -3glox + 10goL + goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-4l + -3lx + 10L + 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 + -3lx + 10L + xL)' equal to zero and attempt to solve: Simplifying -4l + -3lx + 10L + xL = 0 Reorder the terms: 10L + -4l + -3lx + xL = 0 Solving 10L + -4l + -3lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-10L' to each side of the equation. 10L + -4l + -3lx + -10L + xL = 0 + -10L Reorder the terms: 10L + -10L + -4l + -3lx + xL = 0 + -10L Combine like terms: 10L + -10L = 0 0 + -4l + -3lx + xL = 0 + -10L -4l + -3lx + xL = 0 + -10L Remove the zero: -4l + -3lx + xL = -10L Add '4l' to each side of the equation. -4l + -3lx + 4l + xL = -10L + 4l Reorder the terms: -4l + 4l + -3lx + xL = -10L + 4l Combine like terms: -4l + 4l = 0 0 + -3lx + xL = -10L + 4l -3lx + xL = -10L + 4l Add '3lx' to each side of the equation. -3lx + 3lx + xL = -10L + 4l + 3lx Combine like terms: -3lx + 3lx = 0 0 + xL = -10L + 4l + 3lx xL = -10L + 4l + 3lx Add '-1xL' to each side of the equation. xL + -1xL = -10L + 4l + 3lx + -1xL Combine like terms: xL + -1xL = 0 0 = -10L + 4l + 3lx + -1xL Simplifying 0 = -10L + 4l + 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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