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

          >>>> The plural of mongoose begins with p. <<<<