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Simplifying log(4 + -2x) + log(9 + -3x) = 2log(x + 1) (4 * glo + -2x * glo) + log(9 + -3x) = 2log(x + 1) (4glo + -2glox) + log(9 + -3x) = 2log(x + 1) 4glo + -2glox + (9 * glo + -3x * glo) = 2log(x + 1) 4glo + -2glox + (9glo + -3glox) = 2log(x + 1) Reorder the terms: 4glo + 9glo + -2glox + -3glox = 2log(x + 1) Combine like terms: 4glo + 9glo = 13glo 13glo + -2glox + -3glox = 2log(x + 1) Combine like terms: -2glox + -3glox = -5glox 13glo + -5glox = 2log(x + 1) Reorder the terms: 13glo + -5glox = 2glo(1 + x) 13glo + -5glox = (1 * 2glo + x * 2glo) 13glo + -5glox = (2glo + 2glox) Solving 13glo + -5glox = 2glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glo' to each side of the equation. 13glo + -2glo + -5glox = 2glo + -2glo + 2glox Combine like terms: 13glo + -2glo = 11glo 11glo + -5glox = 2glo + -2glo + 2glox Combine like terms: 2glo + -2glo = 0 11glo + -5glox = 0 + 2glox 11glo + -5glox = 2glox Add '-2glox' to each side of the equation. 11glo + -5glox + -2glox = 2glox + -2glox Combine like terms: -5glox + -2glox = -7glox 11glo + -7glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 11glo + -7glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(11 + -7x) = 0Subproblem 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 + -7x)' equal to zero and attempt to solve: Simplifying 11 + -7x = 0 Solving 11 + -7x = 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 + -7x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -7x = 0 + -11 -7x = 0 + -11 Combine like terms: 0 + -11 = -11 -7x = -11 Add '7x' to each side of the equation. -7x + 7x = -11 + 7x Combine like terms: -7x + 7x = 0 0 = -11 + 7x Simplifying 0 = -11 + 7x 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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