Limits of Sequences with Logarithms

For the limits of many sequences with logarithms, you can confidently use the transformations and formulas for logarithms learned in high school. For example:

Example of a Limit of a Sequence with Logarithms


In situations where logarithms had different bases and there wasn’t much you could do about it, they were converted to a common base using the formula: . For our limit, it will be nice and convenient to take this base: . We then have the limit of the sequence:


We know that , which in our expression is . Therefore:


And this expression, using the high school formula again (but this time in reverse), will be equal to …


Which is of course the result (an irrational number).

There was no need to use any limit methods – just the high school logarithm transformations were enough.

Want to know more about calculating limits? I recommend my course 🙂

Krystian Karczyński

Założyciel i szef serwisu eTrapez.

Magister matematyki Politechniki Poznańskiej. Korepetytor matematyki z wieloletnim stażem. Twórca pierwszych Kursów eTrapez, które zdobyły ogromną popularność wśród studentów w całej Polsce.

Mieszka w Szczecinie. Lubi spacery po lesie, plażowanie i kajaki.

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