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