You want to take a logarithm in various bases.
For logarithms to base e, use the built-in log:
> (log (exp 2))
2
> (log 2.718281828)
Note that
log is often called
ln in the mathematical literature.
R5RS Scheme mandates the presence of natural logarithm (ln, which is written
log in Scheme). If you want logarithms in some other base you need to use the standard mathematical relation:
log(x)
log (x) = ---------
n log(n)
Example:
To find the base 10 logarithm of 1.82:
log(1.82)
log (1.82) = -----------
10 log(10)
> (/ (log 1.82) (log 10))
0.2600713879850748
The most common bases besides e is 2 and 10. These logarithms are often
called
log2 and
log10.
(define (log2 x)
(/ (log x) (log 2))
(define (log10 x)
(/ (log x) (log 10))
To avoid recomputation of the denominator at each call, one can use:
(define log2
(let ([denom (log 2)])
(lamdda (x)
(/ (log x) denom))))
(define log10
(let ([denom (log 10)])
(lamdda (x)
(/ (log x) denom))))
A general version is:
(define (log-n n x)
(/ (log x) (log n)))
> (log-n 10 1.82)
0.2600713879850748
Names modified per your suggestion. :-)
--
BrentAFulgham - 14 May 2004
I recently had to make this
log10. Too bad log information isn't preserved as part of exactness. :)
(define log10 (let ((ln-10 (log 10))) (lambda (n) (/ (log n) ln-10))))
I second the idea of a library for this. Actually, a couple of these
log functions
really belong in
MzLib? if not
MzScheme default environment, IMHO.
--
NeilVanDyke - 14 May 2004
By the way, I'd suggest not planting the idea of using underscores in Scheme identifiers, even though underscore makes sense to
TeX? users in the case of
log_e. How about
log-e or
loge?
--
NeilVanDyke - 14 May 2004
I reformatted the math formulas. I had an itch to change
log-n to
logn.
The
- will disturb my eye in a mathematical context. Besides, the names
log2 and
log10 are the traditional ones.
--
BrentAFulgham - 14 May 2004
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