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Simplifying log(3x + 2) + log(4) = log(11x + 12) Reorder the terms: glo(2 + 3x) + log(4) = log(11x + 12) (2 * glo + 3x * glo) + log(4) = log(11x + 12) (2glo + 3glox) + log(4) = log(11x + 12) Reorder the terms for easier multiplication: 2glo + 3glox + 4glo = log(11x + 12) Reorder the terms: 2glo + 4glo + 3glox = log(11x + 12) Combine like terms: 2glo + 4glo = 6glo 6glo + 3glox = log(11x + 12) Reorder the terms: 6glo + 3glox = glo(12 + 11x) 6glo + 3glox = (12 * glo + 11x * glo) 6glo + 3glox = (12glo + 11glox) Solving 6glo + 3glox = 12glo + 11glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12glo' to each side of the equation. 6glo + -12glo + 3glox = 12glo + -12glo + 11glox Combine like terms: 6glo + -12glo = -6glo -6glo + 3glox = 12glo + -12glo + 11glox Combine like terms: 12glo + -12glo = 0 -6glo + 3glox = 0 + 11glox -6glo + 3glox = 11glox Add '-11glox' to each side of the equation. -6glo + 3glox + -11glox = 11glox + -11glox Combine like terms: 3glox + -11glox = -8glox -6glo + -8glox = 11glox + -11glox Combine like terms: 11glox + -11glox = 0 -6glo + -8glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(3 + 4x) = 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 '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Add '-4x' to each side of the equation. 4x + -4x = -3 + -4x Combine like terms: 4x + -4x = 0 0 = -3 + -4x Simplifying 0 = -3 + -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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