Logarithm Table

From WikiEducator

Jump to:navigation, search

Created by Paul Tauriki on 02-07-08.

Significant figures
Wikipedia has an article on this subject.

Visit Significant figures for more in depth information

{{Wikipedia|Significant figures}}




Key points

Steps taken to create Logarithm Table.pdf:

  1. Created Logarithm Table in MS Exel 2003
  2. Exported exel file to MS Word 2003
  3. Opened MS Word file in Open Write and saved as Open Write file
  4. Exported Open Write file to PDF file (Lossless)



The following is a Logarithm Table with values rounded to three significant figures for numbers between 1 and 10. In order to use it for numbers less than one and greater than ten, the numbers have to be rounded first to three significant figures then converted to Standard Form before reading the logarithm values from the table.

View Logarithm Table in PDF format

Instructions on How to use the Logrithm Table

This is a technique to simplify harder Maths operations such as multiplications and divisions. Instead of doing multiplication we will do the addition and instead of doing division we will do the subtraction.

Adding instead of Multiplying

Using the Indice Identity where

(Note that the bases are the same)

Similarly

For example

First of all we need to convert the above to Standard Form, which is

Now if we look up in the logrithm table for 2.39 we will find 0.378 and looking up 5.67 gives us 0.754. These means

2.39 = 100.378 and
5.67 = 100.754.

Replacing 2.39 with 100.378 and 5.67 with 100.754 in the above and discarding the brackets, we will have

= 100.378 + 1 + 0.754 + 2
= 104.132

This can be written as

.

We need to convert back 100.132 reading the table backward. Reading 0.132 from the table but reading it backward i.e find 0.132 in the body of the table and read the number (from right and top) gives us 1.355, since 1.32 lies between 1.30 and 1.34. Replacing 100.132 with 1.355 in the above gives us

. This is the same as 13550. Since the table values are rounded to three significant numbers so our answer should be 13600 (3 s.f.).

Subtracting instead of Dividing

Recall another Indice Identity which is:

, for a ≠ 0

Similarly we can have

For example

Converting the above to Standard Form gives us

Looking up the Logarithm Table for 9.78 gives us 0.990 and 4.5 gives us 0.653. This means that 9.78 = 100.990 and 4.5 = 100.653. Replacing into the above gives us

This can be written as

Now we look up 0.337 in the table but reading the table backwards gives us 2.175 since 0.337 is between 0.336 and 0.338. Substituting into the above gives us

. So our answer is 21.75 but when rounded to 3 significant figures we get 21.8 (3 s.f.).
Create a book
Bookmark and Share