Multiple choice

The roots of the equation log2 (x2 - 4x - 1) = 2 are:

  1. 4, 5

  2. 2, -3

  3. -1, 5

  4. 3, 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

log2(x^2 - 4x - 1) = 2 implies x^2 - 4x - 1 = 2^2 = 4. So, x^2 - 4x - 5 = 0. Factoring gives (x - 5)(x + 1) = 0. The roots are x = 5 and x = -1.

AI explanation

Convert the logarithmic equation into its exponential form to get x^2 - 4x - 1 = 2^2, which simplifies to x^2 - 4x - 5 = 0. Factor the quadratic equation to find the roots: (x - 5)(x + 1) = 0. Solving this gives the roots as -1 and 5.

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