To solve this equation for x, we can first simplify the expression on the right side by using the properties of logarithms. We know that log(a^m) = m*log(a) and log(ab) = log(a) + log(b).

Given,

log(1/2x) = 2/3log(a) - 1/5log(1/2b)

log(1/2x) = log(a^(2/3)) - log((1/2b)^(1/5))

log(1/2x) = log((a^2)^(1/3)) - log((1/2)^(1/5)*b^(1/5))

log(1/2x) = log((a^2)^(1/3)) - log((1/2)^1*(b)^(1/5))

log(1/2x) = log(a^(2/3)) - log(1/2)*log(b)^1/5

Using the rules of logarithms, we can simplify further,

log(1/2x) = log(a^(2/3)) - log(1/2)*log(b)

Now, we can equate the arguments of the logarithms to solve for x,

1/2x = a^(2/3)/(1/2*b)

1/2x = 2a^(2/3)/b

x = 4a^(2/3)/b

Therefore, x = 4a^(2/3)/b.