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Simplifying 2log(x + 1) + -1log(x + 2) = log(2x + -1) Reorder the terms: 2glo(1 + x) + -1log(x + 2) = log(2x + -1) (1 * 2glo + x * 2glo) + -1log(x + 2) = log(2x + -1) (2glo + 2glox) + -1log(x + 2) = log(2x + -1) Reorder the terms: 2glo + 2glox + -1glo(2 + x) = log(2x + -1) 2glo + 2glox + (2 * -1glo + x * -1glo) = log(2x + -1) 2glo + 2glox + (-2glo + -1glox) = log(2x + -1) Reorder the terms: 2glo + -2glo + 2glox + -1glox = log(2x + -1) Combine like terms: 2glo + -2glo = 0 0 + 2glox + -1glox = log(2x + -1) 2glox + -1glox = log(2x + -1) Combine like terms: 2glox + -1glox = 1glox 1glox = log(2x + -1) Reorder the terms: 1glox = glo(-1 + 2x) 1glox = (-1 * glo + 2x * glo) 1glox = (-1glo + 2glox) Solving 1glox = -1glo + 2glox 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. glo + 1glox = -1glo + glo + 2glox Combine like terms: -1glo + glo = 0 glo + 1glox = 0 + 2glox glo + 1glox = 2glox Add '-2glox' to each side of the equation. glo + 1glox + -2glox = 2glox + -2glox Combine like terms: 1glox + -2glox = -1glox glo + -1glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(1 + -1x) = 0Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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