What is the result of dividing log(log x) by log x?

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SUMMARY

The discussion focuses on the mathematical expression [log(log x)] / [log x]. Participants clarify that this expression does not simplify to log(x) or any other simpler form. The consensus is that log(log(x)) does not equal (log(x))^2, and thus the expression remains as is. The analogy provided compares this to the expression [sin(sin x)] / [sin x], emphasizing that simplification is not valid in either case.

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what is: [log(log x)] / [log x]i would guess logx/1 but not sure
 
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GlobalDuty said:
what is: [log(log x)] / [log x]


i would guess logx/1 but not sure

No, it's [log(log x)] / [log x]. :-p

\frac{\log\log x}{\log x} doesn't simplify.
 
\frac{log(log(x))}{log(x)} would equal log(x) if log(log(x))=(log(x))^2=log(x)log(x), but it doesn't :-p

It's the same deal as trying to simplify say, \frac{sin(sinx)}{sinx} this doesn't equal sin(x) because the numerator is not sin2(x)
 

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