Find the value of x that satisfies the equation log₃(x + 1) + log₃(x - 1) = log₃ 8.

Model Answer & Options

Source: Extra Practice

x = 3

x = -3

x = ±3

x = 9

Explanation

Using the product rule log a + log b = log(ab), we get log₃((x + 1)(x - 1)) = log₃ 8. This implies (x + 1)(x - 1) = 8, so x² - 1 = 8, which means x² = 9. This gives x = 3 or x = -3. However, the domain of a logarithm requires the argument to be positive. If x = -3, (x+1) and (x-1) are negative, making the original logs undefined. Thus, only x = 3 is valid.

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