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Simplifying log(-2x + -6) = log(x + 9) Reorder the terms: glo(-6 + -2x) = log(x + 9) (-6 * glo + -2x * glo) = log(x + 9) (-6glo + -2glox) = log(x + 9) Reorder the terms: -6glo + -2glox = glo(9 + x) -6glo + -2glox = (9 * glo + x * glo) -6glo + -2glox = (9glo + glox) Solving -6glo + -2glox = 9glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9glo' to each side of the equation. -6glo + -9glo + -2glox = 9glo + -9glo + glox Combine like terms: -6glo + -9glo = -15glo -15glo + -2glox = 9glo + -9glo + glox Combine like terms: 9glo + -9glo = 0 -15glo + -2glox = 0 + glox -15glo + -2glox = glox Add '-1glox' to each side of the equation. -15glo + -2glox + -1glox = glox + -1glox Combine like terms: -2glox + -1glox = -3glox -15glo + -3glox = glox + -1glox Combine like terms: glox + -1glox = 0 -15glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '-3glo'. -3glo(5 + x) = 0 Ignore the factor -3.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 '(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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