[gms7777]

I agree with you. I only meant to refer to the (log(x))^2 case as nonsensical, though I think my wording was ambiguous. I understand its a hort-cut but it doesn't make mathematical sense as a notation. I think it makes more in the log(log(x)) case, for the same reasons you've pointed out. Though, at least in my experience in my field (theoretical CS), I see it used as (log(x))^2 far more often than log(log(x)).

[pjakma]

Yes, log^2(x) seems almost always to be used to mean [log(x)]^2 in the routing theory papers I tend to read.

I agree with you though that using log^2(x) for [log(x)]^2 is horridly ambiguous notation that should be avoided! (Which reminds me, I should go and check my thesis for this ;) ).