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Simplifying g(x) = log(x + -6) Multiply g * x gx = log(x + -6) Reorder the terms: gx = glo(-6 + x) gx = (-6 * glo + x * glo) gx = (-6glo + glox) Solving gx = -6glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '6glo' to each side of the equation. 6glo + gx = -6glo + 6glo + glox Combine like terms: -6glo + 6glo = 0 6glo + gx = 0 + glox 6glo + gx = glox Add '-1glox' to each side of the equation. 6glo + -1glox + gx = glox + -1glox Combine like terms: glox + -1glox = 0 6glo + -1glox + gx = 0 Factor out the Greatest Common Factor (GCF), 'g'. g(6lo + -1lox + x) = 0Subproblem 1
Set the factor 'g' equal to zero and attempt to solve: Simplifying g = 0 Solving g = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g = 0Subproblem 2
Set the factor '(6lo + -1lox + x)' equal to zero and attempt to solve: Simplifying 6lo + -1lox + x = 0 Solving 6lo + -1lox + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6lo' to each side of the equation. 6lo + -1lox + -6lo + x = 0 + -6lo Reorder the terms: 6lo + -6lo + -1lox + x = 0 + -6lo Combine like terms: 6lo + -6lo = 0 0 + -1lox + x = 0 + -6lo -1lox + x = 0 + -6lo Remove the zero: -1lox + x = -6lo Add 'lox' to each side of the equation. -1lox + lox + x = -6lo + lox Combine like terms: -1lox + lox = 0 0 + x = -6lo + lox x = -6lo + lox Add '-1x' to each side of the equation. x + -1x = -6lo + lox + -1x Combine like terms: x + -1x = 0 0 = -6lo + lox + -1x Simplifying 0 = -6lo + lox + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
g = {0}
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