Logarithm of Numbers less than

Find: Log 0.21

• To determine this logarithm, we must subtract 1 from Log 2.1. Subtracting 1 from the logarithm is the same as moving the decimal point one place to the left … or the same as dividing by 10.
• Log 0.21 = 0.322 – 1.000 = – 0.678

Find: Log 0.00021

• We now have a decimal point 4 places to the left of 2.1.
• Thus, we subtract 4 from Log 2.1
• 0.322 – 4.000 = – 3.678

General procedure for determining logarithms of numbers less than 1:

Determine the mantissa of the number as if it were between 1 and 10, using your L scale. Then subtract the characteristic for the number of places the decimal point of your actual number is to the left of the whole single digit number.

In the example above, the decimal point for 0.00021 is 4 places to the left of the whole single digit number 2.1. So we subtract 4.