The way we write ln(x) to the power of a

[johann1301]

I have learned that (cos x)^a can be written as cos^ax. And like wise for sin x and tan x.

How come we don't write (ln x)^a as ln^ax or (log x)^a as log^ax?

I just think it seems smarter when its written with as few symbols as possible.

(Or perhaps its just my textbook which don't write it this way?)

Thanks in advance!

 

[arildno]

LOTS of textbooks use that convention. I will go as far as to say it is the most common convention.

 

[Mentallic]

Personally, I hardly ever see logs with powers (except in a couple of circumstances), while trigs with powers (especially squared) are a common occurrence.

 

[Office_Shredder]

My advisor has gone so far as to tell me when I square any function I should write it as f²(x), which I personally don't like but what am I going to do about it (I would rather write f(x)²). I will admit that it makes the final writeup a little cleaner looking

 

[eigenperson]

The notation f^a(x) is a little bit ambiguous because it can mean either f(x)^a or f(f(...f(x)...)).

You can usually work out the meaning from context. If f is a trig function, you are probably okay, since in most situations it does not make sense to iterate the sine function. But both log(log(x)) and (log(x))² are potentially useful things.