How do we find Log2000 and Log0.22 using *Log Table* ?
Answers
Answer:
Step-by-step explanation:
The logarithm of a number is made up of two parts:
1. characteristic (to the left of the decimal)
2. mantissa (to the right of the decimal)
e.g. log(34) = 1.5314
The characteristic is determined by counting the number of non-zero digits before the decimal, and substrating "1" from this number.
"34" has two places before the decimal, which is why the characteristic is 2-1 = 1.
While looking up the log table, you will only look at "34". As there are no more digits. Come to the row showing "34" and look under "0" (because there is nothing after 34 in the given number).
The log table gives you the mantissa while the characteristic has to be determined by you.
The mantissa is "5315"
Thus, log(34) = 1.5315
Let us now find log(3.4)
The characteristic is "0" as there is only one digit (which is 3) before the decimal, characteristic = number of digits - 1 = 1-1 = 0
When we are finding the mantissa, we treat 3.4 just as 34. This is important!
So, the mantissa would again be "5315"
Thus, log(3.4) = 0.5315
Remember: while finding mantissa, please ignore the decimal and treat the number as one unit, starting from the first non-zero digit.
It is easy to see that log(3400) = 3.5315
Coming to your example:
log(2000) = ?
There are four non-zero digits before the decimal. Thus, the characteristic is 4-1 = 3
In the log table, come to row showing "20" and look under "0" and then again under "0" (in the second set of columns)
log(2000) = 3.3010
log(0.22) = ?
Here, there are NO significant digits before the decimal point, hence the characteristic will be 0 - 1 = -1.
Such a characteristic is denoted as "Bar 1", which is 1 with a bar on top. I am writing it as 1 because I cannot easily find the key mapping here. Please note that "bar 1" does not mean "negative". It is something like the "negative" sign but applicable ONLY to the characteristic and not the mantissa.
For the mantissa, we find that of "22" which is "3424"
Hence, log(0.22) = 1.3424
In calculators, there is no concept of "bar". The number is therefore expressed as -0.6575. Here the minus sign is used in its real sense.
I am not sure how much I have been able to help, but I trust this will help you get started at least.