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Simplifying log(x + 5) + -1log(x + -1) = log(x + 1) Reorder the terms: glo(5 + x) + -1log(x + -1) = log(x + 1) (5 * glo + x * glo) + -1log(x + -1) = log(x + 1) (5glo + glox) + -1log(x + -1) = log(x + 1) Reorder the terms: 5glo + glox + -1glo(-1 + x) = log(x + 1) 5glo + glox + (-1 * -1glo + x * -1glo) = log(x + 1) 5glo + glox + (1glo + -1glox) = log(x + 1) Reorder the terms: 5glo + 1glo + glox + -1glox = log(x + 1) Combine like terms: 5glo + 1glo = 6glo 6glo + glox + -1glox = log(x + 1) Combine like terms: glox + -1glox = 0 6glo + 0 = log(x + 1) 6glo = log(x + 1) Reorder the terms: 6glo = glo(1 + x) 6glo = (1 * glo + x * glo) 6glo = (1glo + glox) Solving 6glo = 1glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glo' to each side of the equation. 6glo + -1glo = 1glo + -1glo + glox Combine like terms: 6glo + -1glo = 5glo 5glo = 1glo + -1glo + glox Combine like terms: 1glo + -1glo = 0 5glo = 0 + glox 5glo = glox Add '-1glox' to each side of the equation. 5glo + -1glox = glox + -1glox Combine like terms: glox + -1glox = 0 5glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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