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Here's a little recursive algorithm due to John Napier (16th century).

//Globals defined outside of function for clarity
static double aMean = -1.0; //arithmetic mean
static double gMean = -1.0; //geometric mean
static double precision = 0.00001; //adjustable precision

n is the number whose log is sought
b1 and b2 are two boundary values where b1 < n < b2
l1 and l2 are the known logs of b1 and b2, respectively

double rLog(double n, double b1, double b2, double l1, double l2) {
if( abs(b1 - b2) > precision ) {
gMean = sqrt( b1 * b2 );
aMean = ( l1 + l2 ) / 2;
if( n <= gMean ) rLog(n, b1, gMean, l1, aMean);
else rLog(m, gMean, b2, aMean, l2);
return aMean;

Invoking, say, recLog(100, 10, 1000, 1, 3) gives 1.99999 or so. (Be wary of numberical errors)

Edited by - Graylien on June 28, 2001 9:59:41 PM

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thanx alot, graylien. that''s exactly what i was looking for.

To the vast majority of mankind, nothing is more agreeable than to escape the need for mental exertion... To most people, nothing is more troublesome than the effort of thinking.

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