As @egreg pointed out in the comments, to avoid ambiguity a pair of parentheses is recommended. Or maybe you could try $\max_{x\ge2} -{\log x}$
instead of the full expression $\max\{ \, -{\log x} : x\ge2 \, \}$
.
You mentioned you wanted a unary negation, so you have to use $-{\log x}$
, and even $-\log x$
is incorrect.
In the $-\log x$
example, \log
is of class \mathop
, and the minus sign (which is not a binary operation here) will be rendered as an ordinary object (class \mathord
- see this answer to learn about math classes). And so a thin space \,
is added between them (because a thin space is always inserted between \mathord
and \mathop
- see this answer - think $\sin x\cos x$
for example).
Therefore, to truly get unary negation, you must make sure whatever you are negating is itself an ordinary object. This can be done by simply enclosing \log x
within a pair of {}
. Same idea applies to $-{\sin x}$
, $\tan x = {\sin x}/{\cos x}$
, etc.
\max(-\log x)
$\max -\log x$
as opposed to$\max -b$
.\max\log x
, because there's no binding of the variable. I can suggest\max-{\log x}
,\max\{\log x:x>0\}
(or whatever interval you compute the maximum over.\max{}-\log x
? I dislike, but...