To find the value of x, we can set the two equations equal to each other:

(0.5)^x = 1/64 and (3/7)^(3x-7) = (7/3)^(7x-3)

For the first equation:

0.5 = 1/(2^6) = 2^(-6)
So, we can rewrite the equation as:
2^(-6x) = 2^(-6)

This implies that -6x = -6 which means x = 1

For the second equation:

(3/7)^(3x-7) = (7/3)^(7x-3)
(3/7)^(3x-7) = (3/7)^-(7x-3)

This implies that 3x - 7 = -7x + 3
10x = 10
x = 1

Therefore, the solution is x = 1.