To simplify the given expression:

3(log10^2 - log10^24) / (log10^3 + log10^27)

Using the properties of logarithms, we can rewrite log10^2 and log10^24 as:

log10^2 = 2
log10^24 = 24

Now the expression becomes:

3(2 - 24) / (3 + 27)

Simplify the expression further:

3(-22) / 30
-66 / 30
-11 / 5

Therefore, the simplified expression is -11/5.