Log Tables

A logarithm is simply an index (or power).  'Natural' logarithms as used by Napier are in base 'e' (a natural number that just goes on like pi without recurring, and is  just over 2.718 ..... ). 

But a simple log table of base 2 might be easier to explain how logarithms work.

Make your own set of logarithms as follows, these are logarithms to base 2:

So

2 to the power of 1 is two

2 to the power of 2 is four

2 to the power of 3 is 8

2 to the power of 4 is 16

2 to the power of five is 32.

Now to multiple 4x8, use the powers, these are the logarithms

Therefore:

Log (base 2) of    4 is 2

Log(base 2) of     8 is 3

Log (base 2) of 16 is 4

Log (base 2) of 32 is 5

To multiply 4x8, use the logs of 4 and 8 and add them together which equals 3+2 which is equal to 5.  Then do the reverse to find the antilog (ie find out what two the power of five is by looking it up on the above table.

The antilog (base 2) of 5 is found to be 32 by looking at the table in reverse.

which is the sum we wanted to do, 4x8.

ie, 2 to the power of two multiplyed by 2 to the power of three is equal to 2 to the power of five which equals 32, which is 4x8

You could make up your own set of logarithms like this, but they would only be useful for multiplying powers of two together.  Intermediate numbers use fractional indexes (powers) which would take an awful long time to work out manually).

Hope this explains it a bit.  I read the wikipedia article and it was perhaps a little confusing if you don't understand what they are saying. The above is how I learned what logarithms are at school fifty years ago and I can remember it as clearly as anything.  We wrote the powers of two down to 2 to the power of thirty, which is a few million over 1000,000,000. (which was one thousand million when I was at school, a billion was one million million in those far off days!

A logarithm is simply an index (or power).  'Natural' logarithms as used by Napier are in base 'e' (a natural number that just goes on like pi without recurring, and is  just over 2.718 ..... ). 

But a simple log table of base 2 might be easier to explain how logarithms work.

Make your own set of logarithms as follows, these are logarithms to base 2:

So

2 to the power of 1 is two

2 to the power of 2 is four

2 to the power of 3 is 8

2 to the power of 4 is 16

2 to the power of five is 32.

Now to multiple 4x8, use the powers, these are the logarithms

Therefore:

Log (base 2) of    4 is 2

Log(base 2) of     8 is 3

Log (base 2) of 16 is 4

Log (base 2) of 32 is 5

To multiply 4x8, use the logs of 4 and 8 and add them together which equals 3+2 which is equal to 5.  Then do the reverse to find the antilog (ie find out what two the power of five is by looking it up on the above table.

The antilog (base 2) of 5 is found to be 32 by looking at the table in reverse.

which is the sum we wanted to do, 4x8.

ie, 2 to the power of two multiplyed by 2 to the power of three is equal to 2 to the power of five which equals 32, which is 4x8

You could make up your own set of logarithms like this, but they would only be useful for multiplying powers of two together.  Intermediate numbers use fractional indexes (powers) which would take an awful long time to work out manually).

Hope this explains it a bit.  I read the wikipedia article and it was perhaps a little confusing if you don't understand what they are saying. The above is how I learned what logarithms are at school fifty years ago and I can remember it as clearly as anything.  We wrote the powers of two down to 2 to the power of thirty, which is a few million over 1000,000,000. (which was one thousand million when I was at school, a billion was one million million in those far off days!