how to study the logarithms table

how to study the logarithms table


2 Answers

askIITians Faculty 1246 Points
7 years ago
Assuming that you have a table of 4-figure logarithms to base 10 (known as Common Logarithms) with numbers 10 to 99 down the left hand column, and 1-9 across the top of the main columns, with a further 9 narrower columns headed 1-9 to the right of these. The right hand columns are known as 'proportional parts' or 'differences'.

Let's suppose you want to find log(413.9).

Write the number in scientific notation, with one digit left of the decimal point and a power of 10 following:
413.9 = 4.139 * 10^2.
The power 2 in 10^2 indicates that the decimal point needs to be moved 2 places right.

For 0.0003182, it would be 3.182 * 10^(-4) as the decimal point has to be moved left 4 places.

The power of 10 is the first digit to write down in your logarithm, before you even look at the table. If it's negative, you don't write 'minus' in front, you put a horizontal line or bar over the top. The decimal portion of the logarithm, which you get from the table, is always positive.

log(413.9) starts with '2.' That number to the left of the decimal point is known as the 'characteristic'. If it is negative 4, you read it as 'bar 4'.

Now to the table to get the decimal portion. Look down the left hand column of the table for 41 and find the table entry under the column headed 3 (that's the 3rd. digit in your number). Keep your finger on that number (6160), and read the number (9) under 9 (the last digit of your number) in the columns on the right. Add the 9 on to the 6160 giving 6169 as the decimal portion (mantissa) of your logarithm. Your complete logarithm is 2.6169.

When the power of 10 in the original number is negative, the logarithm you obtain from the table will look different from that given by a calculator. A calculator gives:
log(0.0003182) = - 3.4973.
From tables you will get:
[bar 4].5027.
110 Points
7 years ago

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