Re: TI-85 (Logarithm)
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Re: TI-85 (Logarithm)
Jeremy Startzer writes:
> Can any tell me how to calculate Log(base x)(n), on the TI-85.
>
> Where "x" is any number besides 10.
>
> Or is the only way is to use "ln(n) / ln(x)"
Gee, we ought to set up a FAQ on this! Here is another way to see why
this is a correct (and easy) way to obtain the desired value.
If y = Log(base x)(n) , then n = x^y (from the meaning of a logarithm).
But x = 10^log(x) (using base-10 logs here for a minute), and substituting
and simplifying we get
n = 10^[y*log(x)]
This means (looking at it backwards) that log(n) = y*log(x), which we
can solve for y to get
y = log(n) / log(x).
Of course we could have used _e_ as a base in the above argument, in which
case the formula would have come out in natural logs, as the poster asks.
Using this formula on a TI-8x calculator is slightly tedious, though you
can calculate the 1/log(x) or 1/ ln(x) factor just once and store it to
a convenient variable to save keypresses if you are going to be calculating
many logarithms to the same non-standard base. On the TI-92, of course,
you can write your own function.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
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