NAME
    logn -  base n logarithm

SYNOPSIS
    logn(x, n [,eps])

TYPES
    x		nonzero real or complex
    n		nonzero real or complex
    eps		0 < real < 1, defaults to epsilon()

    return	real or complex

DESCRIPTION
    Approximate the base n logarithm function of x by a multiple of
    epsilon, the error having absolute value less than 0.75 * eps.

    The base, n, must not be 0 nor 1.

    When x = 2^a is an integer power of 2 and when n = 2^b is an
    integer power of 2, then log2(x, n) will return a/b
    regardless of the value of eps or epsilon().

    If y is a positive integer, logn(x, n, m^-y) will usually be correct
    to the y-th decimal place.

EXAMPLE
    ; print logn(2, 2), logn(4, 2), logn(1024, 2), logn(2^500, 2), logn(1/2^23209, 2)
    1 2 10 500 -23209

    ; print logn(2, 42), logn(1024, 42), logn(2^500, 42), logn(1/2^23209, 42)
    0.18544902341536890054 1.85449023415368900542 92.72451170768445027095 -4304.08638444729681267682

    ; print logn(127, 1/13), logn(23209, sqrt(3)), logn(2^17-19, 17)
    -1.88860925162778125111 18.29998720595030380546 4.15900804831225415076

    ; print logn(-1, 1i), logn(2+3i, 3i+2), logn(2+3i, 3i)
    2 1 0.80360095345990217753-0.25441159318835790311i

    ; print logn(22+3i, 3i), logn(22+3i, 3i, 1e-50)
    0.98489914201047045409-1.28484657882287682702i 0.98489914201047045408-1.28484657882287682702i

    ; print logn(-127, 7), logn(-127i, 7i)
    2.48941971386002223933+1.61445925708078115429i 1.11272593230445294959-1.70545496954177392315i

    ; print logn(2+3i, 4), logn(-2+3i, 4i)
    0.92510992953527304010+0.70893581537286099830i 1.17764179178059522911+0.22287007593665359808i

    ; print logn(2-3i, 4), logn(-2-3i, 4i)
    0.92510992953527304010-0.70893581537286099830i -0.36752510241663632776-1.14080522421220596732i

    ; print logn(17+0.3i, 17, 1e-75), logn(-17-0.3i, 17i, 1e-75)
    1.00005495001021376506+0.00622799102938744640i 0.29734185630294053511-1.26746929577868497155i

LIMITS
    x != 0
    n != 0 && n != 1
    0 < eps < 1

LINK LIBRARY
    NUMBER *qlogn(NUMBER *x, NUMBER *n, NUMBER *eps)
    COMPLEX *c_logn(COMPLEX *x, COMPLEX *n, NUMBER *eps)

SEE ALSO
    ilog, ilogn, ilog10, ilog2, ln, log, log2

## Copyright (C) 2023  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL.  You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## Under source code control:	2023/08/19 09:14:04
## File existed as early as:	2023
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
