How to Use Logarithmic Tablestable, its the same.there are easy steps to use it. the article features the

applications of log to multiply. we will solve using an example

1. 1We use lograthim in calculation so as to simplfy it. 1. Using log you can convert tedious multiplications and division

operations to simple addition and subtraction.2. Exponents and roots become multiplication and divison problems.3.Lograthim is inverse of expontitation . just like subtraction is inverse

of addition.

Some important formulas1. log (A x B)= log A + log B2. log (A / B ) = log A - log B3. log A^X = X log A for power4. log A^(1/X) = (1/X) log A for root 5. log (AxC / BxD) = log A + log C – logB – log D

Q :-- Multiply 23456 and 789101

Express these numbers in the scientific notation

223456x789101 = (2.3456x10^4) x (7.89101x10^5).

Log (2.3456x10^4) x (7.89101x10^5) = . Log 2.3456 + 4log 10 + log

7.89101 + 5 log 10

o So 23456 is expressed as 2.3456 X 10^4 . and 789101 is expressed as 7.89101 X 10^5.

o Here (^) symbol notes "devided to the power or raised to". Only the first four numbers bear importance while finding log. In this case,

the numbers actually are 2.345 and 7.891 tturn to the natural logarithm page.

2. 4in a spare sheet of paper write down the number

3. 54. This 4 is the power of 10

4. 6

Next, find the number 23 in the first column (standing table) of the page. Now move the finger along the row and stop at the place where it coincides with the number placed at the column which has the heading 4. Your figure at this point should be reading 3692.

5. 7

Now, keeping the number in mind, move the finger further to the mean difference columns coinciding with the column headed 5.your finger should be reading 9. now add this 9 to 3692. you get the number 3701. 3692+9=3701

6. 8

Write the number 3701 next to 4. like this- Here 4 is exponent power of 10 of given number 23456.

7. 9

0.3701+ 4.0000 = 4.3701 ( Digits left to decimal are called characteristics and right to decimal are called mentisa

8. 10

Follow the same steps for the number 7.89101 X 10^5.

9. 11

Write the number 5. in a sheet below 4.3701.

10.12

4.3701

11.13

5. this 5 is the power

12.14

Now find the number 78 in the first column. Move the figure along the row so that the number coincides with the column with heading 9. At this point the figure should read the number 8971.

13.15

Move the finger further to the mean difference columns and the figure should point at the number coinciding with the column with reading 1. The finger reads 1.

14.16

Now add the 1 to 8971. (8971+1=8972) The number obtained is 8972. Place it next to 5 like this.

o 4.3701 o 5.8972 (here we add mentisa with mentisa ) and if it is in two digit then

tenths place number is taken over to characterstics.

15.17

Now add them like this.

o 4.3701 o +5.8972 o ---------- 10.2673 o The value is the log value. The final answer is given by the antilog value.

16.18

Turn to the antilog page. In the first column, place finger at the number .26 and move the finger along the row. Move the finger till it is placed at the number coinciding with column heading 7. The finger should read 1849. Further move the finger to the mean difference columns till it coincides with the number column heading 3. the figure should read 1.

17.19

now add the 1 to 1849. the number obtained is 1850.

18.20

this number is written as 1.850. the 10 is written as 10^10. the 10 here is the number before the decimal place after adding the two log values. see steps 24, 25, 26, 27.

19.21

the final answer looks like this-

20.22

1.850 X 10^10

Edit Tips

always do the calculations on a sheet of paper not mentally.while the column may say "mean difference" the number needs to be

added.read the page heading carefully. a log book has about 30 pages and using

the wrong page will give the wrong answer. always.start using the table only when it is in the scientific notation (power to 10).

Edit Warnings :- Important to note

make sure that the readings are from the same row. sometimes we may mix up rows and columns because of the small size and close spacing.

Edit Things You'll Need

logarithmic table or log book or clarks bookspare sheet of paper Q2 - Divide 23456 by 789101log 23456 – log 789101 = 4.3701 – 5.8972 = 0.4729 – 2.0000 =2bar.4729now take anti log of 0.4729 which is 2.971 . so antilog of 2bar.4729 is 2.971* 10^-2