Learn English – “Minus” a logarithm

mathematicsreading-aloud

I have to explain in words this formula:

A = -log(X)

My guesses would be either:

  1. A is the minus logarithm of X
  2. A is minus the logarithm of X

Is one of these expressions, or yet another one, correct?

Best Answer

After a long debate, it's clear that almost everyone normally writes in words A = -log(X) as either of:

A is minus the logarithm of X.

A is (the) negative the logarithm of X.

There is also evidence that some people use one exclusively over the other. It looks like British English favors the former (minus), while American English favors the latter (negative).

The following are also used, albeit not formally accurate:

A is minus logarithm of X

A is (the) negative logarithm of X

The reason for the inaccuracy is that there is only one logarithm, not one positive and one negative from which you could choose. However, this usage seems okay in some contexts, especially those in which logarithms are multiplied by -1 all the time (Chemistry's pH, for instance).

In spoken language, the same is true, often shortening the logarithm of to simply log and the like.

In order to avoid giving the impression that the final result of -log(X) is negative, however, some (not many) authors will use:

A is the opposite of the logarithm of X

This is much less popular than the other choices, and some people may mistake its meaning for exp(X) rather than -log(X).

Conclusion

Do use minus/negative the logarithm in general writing and speaking as it is much more current and understood by almost everyone, while also being formally accurate. In special contexts where the resulting sign issue might be a concern (perhaps elementary algebra), it may be more effective to address the possible misconception in an additional note than to resort to the opposite of form.

References for the unpopular opposite of variation:
http://en.wikipedia.org/wiki/Plus_and_minus_signs#Minus_sign
http://www.google.com/search?q="opposite of the logarithm"

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