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Simplifying log(1 + -1x) + log(2 + -1x) = log(x + 14) (1 * glo + -1x * glo) + log(2 + -1x) = log(x + 14) (1glo + -1glox) + log(2 + -1x) = log(x + 14) 1glo + -1glox + (2 * glo + -1x * glo) = log(x + 14) 1glo + -1glox + (2glo + -1glox) = log(x + 14) Reorder the terms: 1glo + 2glo + -1glox + -1glox = log(x + 14) Combine like terms: 1glo + 2glo = 3glo 3glo + -1glox + -1glox = log(x + 14) Combine like terms: -1glox + -1glox = -2glox 3glo + -2glox = log(x + 14) Reorder the terms: 3glo + -2glox = glo(14 + x) 3glo + -2glox = (14 * glo + x * glo) 3glo + -2glox = (14glo + glox) Solving 3glo + -2glox = 14glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-14glo' to each side of the equation. 3glo + -14glo + -2glox = 14glo + -14glo + glox Combine like terms: 3glo + -14glo = -11glo -11glo + -2glox = 14glo + -14glo + glox Combine like terms: 14glo + -14glo = 0 -11glo + -2glox = 0 + glox -11glo + -2glox = glox Add '-1glox' to each side of the equation. -11glo + -2glox + -1glox = glox + -1glox Combine like terms: -2glox + -1glox = -3glox -11glo + -3glox = glox + -1glox Combine like terms: glox + -1glox = 0 -11glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(11 + 3x) = 0 Ignore the factor -1.Subproblem 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 '(11 + 3x)' equal to zero and attempt to solve: Simplifying 11 + 3x = 0 Solving 11 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 3x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 3x = 0 + -11 3x = 0 + -11 Combine like terms: 0 + -11 = -11 3x = -11 Add '-3x' to each side of the equation. 3x + -3x = -11 + -3x Combine like terms: 3x + -3x = 0 0 = -11 + -3x Simplifying 0 = -11 + -3x 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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