Okay, let's see. I need to evaluate log base 2 of 64. Hmm, logarithms can sometimes be tricky, but I remember that a logarithm log_b(a) answers the question: "To what power do I need to raise b to get a?" So in this case, the question is asking, "2 raised to what power gives me 64?" 

Let me start by recalling the definition of a logarithm. The logarithm log_b(a) is the exponent that you need to apply to the base b to produce the number a. So, if I have log_2(64), I need to find x such that 2^x = 64. 

Alright, let's break down 64 into its prime factors to see how it relates to powers of 2. I know that 64 is a power of 2. Let me think... 2^1 is 2, 2^2 is 4, 2^3 is 8, 2^4 is 16, 2^5 is 32, and 2^6 is 64. Oh, right! So 2^6 equals 64. Therefore, the exponent x must be 6. 

Wait, let me double-check that. If I compute 2 multiplied by itself 6 times: 2*2=4, 4*2=8, 8*2=16, 16*2=32, 32*2=64. Yep, that's six multiplications. So 2^6 is indeed 64. 

Therefore, log_2(64) should be 6. But just to make sure I didn't make a mistake, let me consider if there's another way to approach this problem. Maybe using the change of base formula? The change of base formula states that log_b(a) can be calculated as log_c(a) / log_c(b), where c is any positive number. If I choose c to be 10, then log_2(64) = log_10(64) / log_10(2). 

I know that log_10(64) is approximately 1.806, since 10^1.806 ≈ 64. And log_10(2) is approximately 0.301. So dividing 1.806 by 0.301 gives roughly 6. That matches my previous result. So that's another way to confirm it. 

Alternatively, if I use natural logarithm, ln(64)/ln(2). Let's see, ln(64) is ln(2^6) which is 6*ln(2). So ln(64)/ln(2) is 6*ln(2)/ln(2) = 6. Yep, that also works. 

So all methods point to the answer being 6. I think that's solid. No mistakes here. Just straightforward exponentiation. Maybe if I had a different number, but 64 is a power of 2, so it's straightforward. 

Wait, another way to think about it: since 2^6 = 64, then the logarithm base 2 of 64 is 6. That's the definition. So that's the answer. 

I don't see any other angles here. The problem is pretty straightforward. Maybe if the number wasn't a power of 2, we'd have to use logarithm properties or approximate, but in this case, since 64 is 2^6, it's exact. 

Just to recap: log_2(64) = x => 2^x = 64. Solving for x gives x=6. All checks confirm this. Therefore, the final answer is 6. 

I think that's all. No steps missed, and all methods converge to the same answer. So confident with this result.
Therefore, the value of $\log_264$ is $\boxed{6}$.
</think>