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Simplifying log(2x + -8) = log(6x + 9) Reorder the terms: glo(-8 + 2x) = log(6x + 9) (-8 * glo + 2x * glo) = log(6x + 9) (-8glo + 2glox) = log(6x + 9) Reorder the terms: -8glo + 2glox = glo(9 + 6x) -8glo + 2glox = (9 * glo + 6x * glo) -8glo + 2glox = (9glo + 6glox) Solving -8glo + 2glox = 9glo + 6glox 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. -8glo + -9glo + 2glox = 9glo + -9glo + 6glox Combine like terms: -8glo + -9glo = -17glo -17glo + 2glox = 9glo + -9glo + 6glox Combine like terms: 9glo + -9glo = 0 -17glo + 2glox = 0 + 6glox -17glo + 2glox = 6glox Add '-6glox' to each side of the equation. -17glo + 2glox + -6glox = 6glox + -6glox Combine like terms: 2glox + -6glox = -4glox -17glo + -4glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 -17glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(17 + 4x) = 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 '(17 + 4x)' equal to zero and attempt to solve: Simplifying 17 + 4x = 0 Solving 17 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 4x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 4x = 0 + -17 4x = 0 + -17 Combine like terms: 0 + -17 = -17 4x = -17 Add '-4x' to each side of the equation. 4x + -4x = -17 + -4x Combine like terms: 4x + -4x = 0 0 = -17 + -4x Simplifying 0 = -17 + -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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