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Since e is a number, not a function (the function is exp = lambda x: e^x) then 1/e is not log but one divided by e.

I once was told that using, say, 1/cos for acos is specific to English-speaking countries. Does anyone know about that?

I think you're thinking of the inverse cosine function arccosine. The reciprocal of the cosine function is known as the secant. I do not know if this is specific to English speaking countries. However the Chinese version of wikipedia suggests it is: http://zh.wikipedia.org/zh/反三角函数

If I recall correctly from high school, we used to call 1/cos "secant", or sec(A).

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