Okay, let's see. The question is asking, what power of 4 equals 8? And they want the answer as a common fraction. Hmm. Alright, so I need to find an exponent x such that 4 raised to the power of x equals 8. That is, solve for x in the equation 4^x = 8. Right.

First, I remember that 4 and 8 are both powers of 2. Let me write that down. 4 is 2 squared, so 4 = 2^2. And 8 is 2 cubed, so 8 = 2^3. Maybe if I express both sides of the equation with base 2, it might help me solve for x.

So substituting those into the equation, we have (2^2)^x = 2^3. Using the exponentiation rule (a^m)^n = a^(m*n), the left side becomes 2^(2x). So now the equation is 2^(2x) = 2^3. Since the bases are the same, the exponents must be equal. Therefore, 2x = 3. Solving for x, I divide both sides by 2, so x = 3/2. 

Wait, but let me check that again. If x is 3/2, then 4^(3/2) should be equal to 8. Let's verify. 4^(1/2) is the square root of 4, which is 2. Then 4^(3/2) is (4^(1/2))^3, which is 2^3 = 8. Yes, that works. So x is indeed 3/2. 

Alternatively, maybe there's another way to approach this. Let's take the logarithm of both sides. If 4^x = 8, then taking the natural logarithm of both sides gives ln(4^x) = ln(8). Using the logarithm power rule, that's x*ln(4) = ln(8). Therefore, x = ln(8)/ln(4). Let me compute that. 

But since 8 is 2^3 and 4 is 2^2, ln(8) is ln(2^3) = 3 ln(2), and ln(4) is ln(2^2) = 2 ln(2). So x = (3 ln(2)) / (2 ln(2)) = 3/2. Same result. So that confirms it. 

Another way to think about it: since 4^x = 8, and 4 is 2 squared, we can write 2^(2x) = 2^3, which gives 2x = 3, so x = 3/2. Yep, same answer. 

I don't see any mistakes here. Both methods lead to the same result, so I think 3/2 is the correct answer. Let me just make sure there's no alternative interpretation. The question says "power of 4 equal to 8". So exponent x such that 4^x = 8. Definitely, 4^(3/2) is 8. 

Wait, maybe someone could think of 4^1.5 instead of 4^(3/2). But 1.5 is 3/2, so that's the same. So 3/2 is the exponent. 

Alternatively, could there be a negative exponent or something? Let's see. If x was negative, 4^x would be a fraction, but 8 is greater than 1, so x must be positive. So 3/2 is the only solution here. 

Therefore, after checking multiple methods and verifying the result, I'm confident that the answer is 3/2.
Therefore, the power of 4 that equals 8 is $\boxed{\frac{3}{2}}$.
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