How to find log and antilog values easily?

In this post, you will study, how to find log and antilog values of a given number. Explanation is provided using examples.

Logarithms and Antilogarithms

In higher classes, many times we encounter such numbers which are either too big or too small. So, to make the calculations easy and time saving, we use logarithms form of the number. The changed number can be put to original form by using antilogarithm. It is clear that logarithms and antilogarithms are inverse of each other.

Lets start to know how to find the log and antilog values.

Logarithms

A logarithm of a number is the power to which a given base must be raised to obtain that number. The power is sometimes called the exponent. In other words,

if b^x = y, then x is the logarithm of y to base b.

So, we can write as, b^x = y

Taking log on both sides,

log b^x = log y

x log b = log y

x = log_b y

Antilogarithm

The antilogarithm of a number is the inverse process of finding the logarithms of the same number. If x is the logarithm of a number y with a given base b, then y is the antilogarithm (antilog) of x to the base b.

If x = log_b y,

then y = antilog x

Natural Logarithms and Anti-Logarithms have their base as 2.7183. The Logarithms and Anti-Logarithms with base 10 can be converted into natural Logarithms and Anti-Logarithms by multiplying it by 2.303.

What is characteristic and mantissa part?

Characteristic Part – The whole part is called the characteristic part. If the characteristic of logarithm of any number greater than one is positive and is one less than the number of digits in the left side of the decimal point.

Mantissa Part – The decimal part of the logarithm number for a given number is called the mantissa part, and it should always be a positive value. If the mantissa part is in a negative value, convert into the positive value.

How to convert Antilog into Log?

We are given with a expression, x = antilog(y) or x = 10^y

Since we know that log and antilog are inverse of each other. So,

y = log(x)

How to find log and antilog values using tables?

Log and antilog tables are given above, check the values from that table which are used to solve the examples given below.

How to calculate log using the log table?

Consider a number 15.27, find its log value.

Step 1: Understand the concept of the logarithm. Each log table is only usable with a certain base. The most common type of logarithm table is used is log base 10.

Step 2: Identify the characteristic part and mantissa part of the given number. For example, if you want to find the value of log₁₀ (15.27), first separate the characteristic part and the mantissa part.

Characteristic Part = 15

Mantissa part = 27

Step 3: Use a common log table. Now, use row number 15 and check column number 2 and write the corresponding value. So the value obtained is 1818.

Step 4: Use the logarithm table with a mean difference. Slide your finger in the mean difference column number 7 and row number 15, and write down the corresponding value as 20.

Examples to find log values of given numbers using log table:

1. log 306.5

See the value of 30 in 6 & mean difference in 5.

Add them.

Ans- 2.4867.

Before decimal 2 because in question there are 3 digits before decimal (3-1=2).

2. log 1.3275

See the value of 13 in 2 & mean difference in 7 & 5.

Add them.

Ans- 0.1245.

Before decimal 0 because in question there is 1 digits before decimal (1-1=0).

How to calculate antilog using the antilog table?

Consider a number, 2.6452, find its antilog value.

Step 1: Separate the characteristic part and the mantissa part. From the given example, the characteristic part is 2, and the mantissa part is 6452.

Step 2: To find a corresponding value of the mantissa part use the antilog table. Using the antilog table, find the corresponding value. Now, find the row number that starts with .64, then the column for 5. Now, you get the corresponding value as 4416.

Step 3: From mean difference columns find the value. Again use the same row number .64 and find the value for column 2. Now, the value corresponding to this is 2.

Step 4: Add the values obtained in step 2 and 3, we get 4416 + 2 = 4418.

Step 5: Now insert the decimal point. The decimal point always goes the designated place. For this, you have to add 1 to the characteristic value. Now you get 3. Then add the decimal point after 3 digits, we get 441.8

So the antilog value of 2.6452 is 441.8.

Examples to find antilog values of given numbers using antilog table:

1. antilog 2.4867

See the value of 48 in 6 & mean difference in 7.

Add them.

Ans- 0.3065 x 10³.

Power 3 because in question before decimal there is 2 i.e., 2+1=3 is power.

2. antilog -2.4867

add 1 on left side i.e., 2+1=3 & subtract the right part from 1 i.e.,1-4867=5133.

This becomes antilog 3.5133 where 3 before decimal is of negative sign.

See the value of 51 in 3 & mean difference in 3.

Add them.

Ans: 0.5463 x 10^-2.

Power -2 because 3 is with negative sign i.e., -3+1 = -2.

I hope this post helps you to learn to “how to find the log and antilog values”.

Read more: Conversion in Organic Chemistry Class 12

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