How to Divide Using Logarithms

Logarithms are nothing more than exponents which are expressed in a different way in mathematics. Most students find it really difficult to divide numbers using logarithms but it is just like dividing numbers by using exponents. For instance, 2 raised to power 2 is equal to 4 which can also be expressed as log 2 of 4 is 2. Follow some important methods to help you divide using logarithms.

Things Required:

- Pencil
- Paper
- Table of Common Logarithms


  • 1

    First of all, you have to choose two numbers which you cannot divide easily by using a pencil and paper. For instance, you can take 162 and 82310 as it is hard to divide the latter with the former without the use of a calculator or mathematical table.

  • 2

    It is extremely important for you to express both the numbers in terms of base ten logarithms. Otherwise, you will not be able to find the answer. Simply write 82310 as log 82310 and 162 as log 162.

  • 3

    In order to determine the logarithms of both the numbers, you will have to use the logarithm table. You can easily find the log 82310 in the logarithm table which is equal to 4.9153998. You will have to see log 8.231 so as to get the numbers to the right side of the decimal point. After that, you have to add 4 to the left side of the decimal point.

  • 4

    Repeat the previous step to find the log 162 which is equal to 2.2095150. Now, you have to subtract 2.21 from 4.915. After subtracting, you will get 2.7058637.

  • 5

    Now, you have to go back to the logarithm table in order to find the antilog of the answer 2.7058637. For this, you will have to look up 0.7058637. Then, you have to move the decimal point of the result to the right side by two places. Thus, you will get the answer, 508.

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