To simplify this expression, we can use the properties of logarithms.

We know that log(a) - log(b) = log(a/b) and log(a^n) = n*log(a).

Therefore, the expression can be simplified as follows:

4log(1/23) - 2/3log(1/27) - 2log(1/26)
= log((1/23)^4) - log((1/27)^(2/3)) - log((1/26)^2)
= log(1/279841) - log(1/19683) - log(1/676)

Now, we can combine the logarithms using the properties of logarithms:

log((1/279841) / (1/19683) / (1/676))
= log((19683*676) / 279841)
= log(13317308 / 279841)
= log(47.5)

Therefore, the simplified expression is log(47.5).