Simplifying nested logarithms with any outer base

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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?