An acidic solution with an H + concentration of 10 вЂ“4 is said to have a pH of 4. For example, in chemistry, you speak often of pH, where H is the concentration of available hydrogen ions in a solution-usually a very small fraction. (The logarithm of a fraction is always negative.) If X is expected to be between 0.0 and 1.0, people in these fields would usually say:Д®xpecting that A will be positive. Some mathematically knowledgeable audiences work a lot with the logarithms of small fractions, but for convenience, they prefer to work with positive numbers. With any mathematical audience, you can write:ДЄ is minus log X. 'Minus' and 'negative' aren't quite synonyms: you'll notice that, above, I said 'negative numbers' 'minus numbers' would be considered incorrect even in British English. On the other hand, the comments indicate that 'the negative logarithm ofВ x' is quite often used to mean '-logВ x'. 'The minus logarithm of x' doesn't work because it suggests there's a thing called a 'minus logarithm' and you're taking that function ofВ x. (Conversely, if you want to emphasize that a quantity is positive, you can say, for example, 'plus three' I'm not sure if Americans would prefer 'positive three'.) Since we're happy to take 'two' to 'minus two', we're happy to take 'the logarithm of x' to 'minus the logarithm of x'. Some examples of negative numbers are 'minus one', 'minus two' and so on. In British English, 'minus' does not refer only to the operation of subtraction but also to what programming langauges would call the 'unary minus' operation.

In British English, 'A is minus the logarithm of x' is fine American English would, I think, prefer 'negative' instead of 'minus'. References for the unpopular opposite of variation: 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. ConclusionДo 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. This is much less popular than the other choices, and some people may mistake its meaning for exp(X) rather than -log(X). In order to avoid giving the impression that the final result of -log(X) is negative, however, some (not many) authors will use: In spoken language, the same is true, often shortening the logarithm of to simply log and the like. 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). The reason for the inaccuracy is that there is only one logarithm, not one positive and one negative from which you could choose. The following are also used, albeit not formally accurate: It looks like British English favors the former (minus), while American English favors the latter (negative). There is also evidence that some people use one exclusively over the other. After a long debate, it's clear that almost everyone normally writes in words A = -log(X) as either of:

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