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Simplifying log(3x + 1) + log(4) = log(11x + 12) Reorder the terms: glo(1 + 3x) + log(4) = log(11x + 12) (1 * glo + 3x * glo) + log(4) = log(11x + 12) (1glo + 3glox) + log(4) = log(11x + 12) Reorder the terms for easier multiplication: 1glo + 3glox + 4glo = log(11x + 12) Reorder the terms: 1glo + 4glo + 3glox = log(11x + 12) Combine like terms: 1glo + 4glo = 5glo 5glo + 3glox = log(11x + 12) Reorder the terms: 5glo + 3glox = glo(12 + 11x) 5glo + 3glox = (12 * glo + 11x * glo) 5glo + 3glox = (12glo + 11glox) Solving 5glo + 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. 5glo + -12glo + 3glox = 12glo + -12glo + 11glox Combine like terms: 5glo + -12glo = -7glo -7glo + 3glox = 12glo + -12glo + 11glox Combine like terms: 12glo + -12glo = 0 -7glo + 3glox = 0 + 11glox -7glo + 3glox = 11glox Add '-11glox' to each side of the equation. -7glo + 3glox + -11glox = 11glox + -11glox Combine like terms: 3glox + -11glox = -8glox -7glo + -8glox = 11glox + -11glox Combine like terms: 11glox + -11glox = 0 -7glo + -8glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(7 + 8x) = 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 '(7 + 8x)' equal to zero and attempt to solve: Simplifying 7 + 8x = 0 Solving 7 + 8x = 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 + 8x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 8x = 0 + -7 8x = 0 + -7 Combine like terms: 0 + -7 = -7 8x = -7 Add '-8x' to each side of the equation. 8x + -8x = -7 + -8x Combine like terms: 8x + -8x = 0 0 = -7 + -8x Simplifying 0 = -7 + -8x 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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