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Simplifying log(x + -1) + log(x + 1) = log(x + 5) Reorder the terms: glo(-1 + x) + log(x + 1) = log(x + 5) (-1 * glo + x * glo) + log(x + 1) = log(x + 5) (-1glo + glox) + log(x + 1) = log(x + 5) Reorder the terms: -1glo + glox + glo(1 + x) = log(x + 5) -1glo + glox + (1 * glo + x * glo) = log(x + 5) -1glo + glox + (1glo + glox) = log(x + 5) Reorder the terms: -1glo + 1glo + glox + glox = log(x + 5) Combine like terms: -1glo + 1glo = 0 0 + glox + glox = log(x + 5) glox + glox = log(x + 5) Combine like terms: glox + glox = 2glox 2glox = log(x + 5) Reorder the terms: 2glox = glo(5 + x) 2glox = (5 * glo + x * glo) 2glox = (5glo + glox) Solving 2glox = 5glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glo' to each side of the equation. -5glo + 2glox = 5glo + -5glo + glox Combine like terms: 5glo + -5glo = 0 -5glo + 2glox = 0 + glox -5glo + 2glox = glox Add '-1glox' to each side of the equation. -5glo + 2glox + -1glox = glox + -1glox Combine like terms: 2glox + -1glox = 1glox -5glo + 1glox = glox + -1glox Combine like terms: glox + -1glox = 0 -5glo + 1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-5 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -1x 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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