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Simplifying log(5 + -2x) = log(4x + -9) (5 * glo + -2x * glo) = log(4x + -9) (5glo + -2glox) = log(4x + -9) Reorder the terms: 5glo + -2glox = glo(-9 + 4x) 5glo + -2glox = (-9 * glo + 4x * glo) 5glo + -2glox = (-9glo + 4glox) Solving 5glo + -2glox = -9glo + 4glox 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. 5glo + 9glo + -2glox = -9glo + 9glo + 4glox Combine like terms: 5glo + 9glo = 14glo 14glo + -2glox = -9glo + 9glo + 4glox Combine like terms: -9glo + 9glo = 0 14glo + -2glox = 0 + 4glox 14glo + -2glox = 4glox Add '-4glox' to each side of the equation. 14glo + -2glox + -4glox = 4glox + -4glox Combine like terms: -2glox + -4glox = -6glox 14glo + -6glox = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 14glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(7 + -3x) = 0 Ignore the factor 2.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 '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Add '3x' to each side of the equation. -3x + 3x = -7 + 3x Combine like terms: -3x + 3x = 0 0 = -7 + 3x Simplifying 0 = -7 + 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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