5/2/2023 0 Comments Caret mathIntriguingly, Cajori doesn't document any notations like yours, with the logarithm appearing as a binary operator between the argument and the base. Notation for logarithms is discussed in the second volume of Cajori's book, paragraph 469. Since Cajori died in 1930, his book is currently out of copyright in the U.S., so depending on where you live, you may be able to read and distribute it freely. ![]() ![]() For a glimpse of how our current mathematical vocabulary came to be, check out Florian Cajori's History of Mathematical Notations. The answer, as many people have pointed out, is "historical accident." The evolution of language is a rich, messy process whose details are hard to predict, control, or explain. Logarithms don't nearly reach the same level of importance among all the other functions one might also want specialized notations for.īut why isn't there the missing log symbol too? In particular we use it to write down polynomials, which are very important functions. Having a specialized notation for exponentiation is worthwhile because exponentiation is so common. At some point using names becomes easier - for example a name made up of letters can easily be looked up in an alphabetically arranged index that is much harder if we just use some strange graphical symbol that doesn't have a conventional place in the alphabet. ![]() In any case, the answer is that there are many different functions that one might want a compact notation for, and only so many different symbols that one can reasonably expect people to remember. ^ is just how the superscript is commonly (but not always) represented on computers in context where one has to stick to linear sequences of characters. The mathematical notation is to write the power as a superscript. ^ is not really a mathematical symbol for exponentiation.
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