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Simplifying log(3x + 1) + log(x + -2) = log(4x + 10) Reorder the terms: glo(1 + 3x) + log(x + -2) = log(4x + 10) (1 * glo + 3x * glo) + log(x + -2) = log(4x + 10) (1glo + 3glox) + log(x + -2) = log(4x + 10) Reorder the terms: 1glo + 3glox + glo(-2 + x) = log(4x + 10) 1glo + 3glox + (-2 * glo + x * glo) = log(4x + 10) 1glo + 3glox + (-2glo + glox) = log(4x + 10) Reorder the terms: 1glo + -2glo + 3glox + glox = log(4x + 10) Combine like terms: 1glo + -2glo = -1glo -1glo + 3glox + glox = log(4x + 10) Combine like terms: 3glox + glox = 4glox -1glo + 4glox = log(4x + 10) Reorder the terms: -1glo + 4glox = glo(10 + 4x) -1glo + 4glox = (10 * glo + 4x * glo) -1glo + 4glox = (10glo + 4glox) Add '-4glox' to each side of the equation. -1glo + 4glox + -4glox = 10glo + 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -1glo + 0 = 10glo + 4glox + -4glox -1glo = 10glo + 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -1glo = 10glo + 0 -1glo = 10glo Solving -1glo = 10glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10glo' to each side of the equation. -1glo + -10glo = 10glo + -10glo Combine like terms: -1glo + -10glo = -11glo -11glo = 10glo + -10glo Combine like terms: 10glo + -10glo = 0 -11glo = 0 Divide each side by '-11'. glo = 0 Simplifying glo = 0 The solution to this equation could not be determined.
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