64^x = 1/2

To solve for x, we need to rewrite the left side of the equation in a way that makes it easier to solve. We can rewrite 64 as 2^6 since 2^6 = 64.

Therefore, our equation becomes:

(2^6)^x = 1/2
2^(6x) = 1/2

Now, we can rewrite 1/2 as 2^(-1) because 2^(-1) is the same as 1/2.

This gives us:

2^(6x) = 2^(-1)

Now we can set the exponents equal to each other:

6x = -1

Now, solve for x:

x = -1/6

Therefore, x = -1/6.