how to use the clarks table?

Question

made by orient longman
I just want to know about the logarithm part

Answer 1

Well I tried to find a copy of the Clark's Tables online, to see if they were different than a normal table of logarithms. I failed.

So I'll explain how to use a regular table of logarithms. Hopefully that's what you want.

To find the logarithm of a number using a logarithm table, you have to do a couple of steps. I'm going to show you the long way first so you understand why the short way works.

1) Write the number in scientific notation:

6.02 × 10²³

2) Take the log of it:

log 6.02 × 10²³

3) Use the law of multiplication of logs to break it into two logs (log ab = log a + log b):

log 6.02 + log 10²³

4) Use the law of exponents of logs (log aⁿ = n log a) to bring down the exponent:

log 6.02 + 23 log 10

5) Use the fact that log 10 = 1:

log 6.02 + 23

6) Look up the value of log 6.02 in a table (like http://www.sosmath.com/tables/logtable/logtable.html ):

0.7795965 + 23 = 23.0.7795965

I did it the long way so you can see WHY it works.

In reality, you would just convert the number to scientific notation, look up the first part in a log table (should always be a decimal), and then add that decimal to the power of 10.

6.02 × 10²³ = 23 + log 6.02 = 23.0.7795965

Before scientific calculators, everyone did it this way...thank goodness for calculators huh?