Efficiently Simplifying Nested Logarithms: A Scientist's Guide

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Nested logarithms can be simplified using standard logarithmic formulas, but this does not necessarily shorten the expression. The outer logarithm can be of any base, and while conversions are possible, they do not reduce the overall complexity. The concept of "simplicity" in logarithmic expressions is subjective and varies by individual preference. Ultimately, there is no method to reduce the number of logarithmic operations below two in these cases. Understanding these principles is crucial for efficient manipulation of nested logarithms.
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Outer log could be any base.
 
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You can convert it with the usual formulas for logarithms (do you know them?), but the expression won't get shorter. "Simple" is a matter of taste.
 
mfb said:
You can convert it with the usual formulas for logarithms (do you know them?), but the expression won't get shorter. "Simple" is a matter of taste.
There is no way to reduce the number of logs being done right? No mater what you convert it to, it will still use at least 2 logs?
 
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