Negative logarithm: spacing

Question

The equation $\max - \log x$ renders in a weird way:

The minus is a unary operator (i.e. it means "negative logarithm", and not "the difference between max and log"). So I would expect that it would be closer to "log". That happens for $-b$ as opposed to $a-b$:

Is there a better way than $-\log x$ to write the negative logarithm?

Answer 1

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.

Answer 2

A double pair of braces will do the trick. However, I also prefer to add a pair of parentheses:

\documentclas{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathtools}

\begin{document}

    \begin{align*}
     & \smashoperator{\max_{1 < x < \mathrm e}}{-}{\log x}\\
 & \smashoperator{\max_{1 < x < \mathrm e}} ({-}{\log x})
    \end{align*}%

\end{document}