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If x satisfies the equation 4^(8x) = 256, then x is equal to ______.

1. 1/2
2. log₁₆ 8
3. 2/3
4. log₄ 8

Correct answer: 1/2

Solution

To solve for x, we can rewrite 256 as a power of 4: 256 = 4⁴. Thus, the equation becomes 4^(8x) = 4⁴, leading to 8x = 4. Dividing both sides by 8 gives x = 1/2.

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