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.
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