Yesterday during a lengthy phone call I had some time to explore the bookshelf in my working room at home. One antique item caught my attention: a logarithm book.

As looking into it I can’t believe that we used that to “compute” logarithms in the 70th when I went to high school. It took me some time again to figure out how it works. Nowadays we simply press the logarithm key on our pocket or windows desktop calculator and compute a logarithm without thinking too much about it.

As mentioned in the introduction to this book the tables used in it would show the mantissa for decimal logarithms. Hmmm, what was a mantissa again ?

According to wikipedia a mantissa can be many things. It is also called significand, a word even my Windows Life Writer spell checker doesn’t know. *A ***significand** (also *coefficient** or **mantissa**) is the part of a **floating-point number** that contains its significant digits. Depending on the interpretation of the **exponent**, the significand may be considered to be an **integer** or a **fraction*.

That explanation does not really help, does it ? After further reading I discovered that for computing a decimal ( base 10 ) logarithm the mantissa would be the part of the number behind the comma.

Let’s make a practical example how this book works. For numbers between 100 and 999,99 we know that they can be expressed in a form 10^{2,mmmm} where mmmm would be the mantissa. We know that the integer part of an exponent to base 10 for a number between 100 and 999,999 is 2, thus we are only interested to find the mantissa – that’s what the table in this book actually is doing.

For 501 it tells us that the mantissa is 6998, thus the solution for the decimal logarithm is: 2,6998. After pressing the logarithm button on my pocket calculator I get: 2.6998377258672457172791038131756.

Looks like the book does work ! I just can’t believe that I belong to a generation doing such antique way of computations !

Anyway, in another posting probably next week I show you what “computers” I used as a student.

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