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Simplifying log * x + log(x + 1) = 2log(1 + -1x) Multiply glo * x glox + log(x + 1) = 2log(1 + -1x) Reorder the terms: glox + glo(1 + x) = 2log(1 + -1x) glox + (1 * glo + x * glo) = 2log(1 + -1x) glox + (1glo + glox) = 2log(1 + -1x) Reorder the terms: 1glo + glox + glox = 2log(1 + -1x) Combine like terms: glox + glox = 2glox 1glo + 2glox = 2log(1 + -1x) 1glo + 2glox = (1 * 2glo + -1x * 2glo) 1glo + 2glox = (2glo + -2glox) Solving 1glo + 2glox = 2glo + -2glox 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 + 2glox = 2glo + -2glo + -2glox Combine like terms: 1glo + -2glo = -1glo -1glo + 2glox = 2glo + -2glo + -2glox Combine like terms: 2glo + -2glo = 0 -1glo + 2glox = 0 + -2glox -1glo + 2glox = -2glox Add '2glox' to each side of the equation. -1glo + 2glox + 2glox = -2glox + 2glox Combine like terms: 2glox + 2glox = 4glox -1glo + 4glox = -2glox + 2glox Combine like terms: -2glox + 2glox = 0 -1glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-1 + 4x) = 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 + 4x)' equal to zero and attempt to solve: Simplifying -1 + 4x = 0 Solving -1 + 4x = 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 + 4x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4x = 0 + 1 4x = 0 + 1 Combine like terms: 0 + 1 = 1 4x = 1 Add '-4x' to each side of the equation. 4x + -4x = 1 + -4x Combine like terms: 4x + -4x = 0 0 = 1 + -4x Simplifying 0 = 1 + -4x 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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