Rebuild Logarithm Tables

To keep what we have requires being able to repair and regenerate as needed.

There are at least two ways to rebuild the log tables if it ever becomes necessary.

The first way is kind of a reversed Sieve of Eratosthenes. Starting with the first four prime numbers larger than one, the logs of larger numbers that are not primes numbers can be easily generated.

The log of 16 is

RL1Larger primes can be interpolated according to the instruction in any table of logs.

To increase precision, numbers can be used that are closer to the prime log being searched for.

RL2

The ratio of the prime to the lower boundary (6.4) to the entire interval (7.2 – 6.4) is roughly the same between logarithms and their powers of ten.

RL3

which is much closer to the logarithm of 7.

Or primes can be found by graphing from nearby numbers that can be easily factored.

The second way to rebuild log tables manually is with roots of ten.

RL4

This table shows up much better in its own tab.

Logs150915_Single

The exponent of 10 is on the left-side column and the power to raise to is under the heading at the top.
The algorithm to generate the table is

for (q = 1; q < 9; q++) {
c = 10 ^ (10 ^ (-q))
for (i = 1; i < 11; i++) {
n = c ^ i
}}

Converting back and forth between common logs and natural logs only requires:

RL5

Advertisements
This entry was posted in Math. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s