Log Table: Meaning, How to Use, Find Log Values from 1 to 10

A log table or logarithmic table contains logarithmic values of different numbers that become useful to perform large calculations involving exponents.

The log table 1 to 10 is especially popular for basic calculations. The log table is used as a reference to carry out complex multiplication or division easily by turning them into addition or subtraction operations.

In this article, we will explore logarithmic tables with different bases, understand log values from 1 to 10, and learn how to read log table data effectively for accurate calculation.

Why Do We Use a Log Table? 

Suppose you are trying to multiply two big numbers like 456 × 789 without a calculator. It can take a very long time! That’s where the log table helps. It helps to solve hard math like multiplication and division to easier ones like adding and subtracting. So, instead of doing a long calculation, you just look up some numbers and add them. This will save time and make math fun.

What is Log Table?

The log table typically contains three types of columns, as mentioned below.

• Main column : It is the first column having numbers from 10 to 99 (all 2-digit numbers).
• Differences column : It is the second set of columns, and it shows the "differences" for the digits 0 to 9.
• Mean difference column: The third set of columns shows the mean differences from 1 to 9.

What is the Meaning of Numbers in the Log Table?

Each and every number in the log table has two parts:

Characteristic – This is the whole number part, which helps you to show how big the number is.

Mantissa – This is the decimal part, which helps you find the exact value of the log number.

Note: Let's assume this is a game, so the characteristic tells you the level you’re on, and the mantissa gives you your score on that level.

The Parts of the Log Value of a Number

Each value in the log table has two parts separated by a decimal point. These two parts are explained below.

• Characteristic : It is the integer part of the value that remains on the left side of the decimal point.
• Mantissa: The part of the value that lies on the right side of the decimal point is called the mantissa.

For example, the value of log 22.35 = 1.3493. Here, 1 is the characteristic and 3493 is the mantissa.

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Log Values 1 to 10

A common logarithm table shows the value of logarithms to the base 10, whereas natural logarithm tables give logarithmic values to the base e (Euler’s number), which is a mathematical constant of the value 2.71828. The values log 1 through 10 with both base 10 and base e are given below.

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Easy Steps to Look at a Log Table

Don’t worry! Reading a log table is very easy. Just follow these easy steps:

1. First, write down your number (like 24.68).

2. Look at the first two digits (24) and find the row.

3. Then look at the next digit (6) and find the column.

4. Find the number where the row and column meet — this is your main value.

5. Look at the mean difference for the last digit (8).

6. Add both values.

7. Add your characteristic, and you get the final answer.

How to Use Log Table? 

It is very important to know how to use the log table to find the log value of a number. The process is explained step-by-step using an example.

Let’s take the example to find out the value of log (24.68)

Step 1: The Integer part is 24 and the decimal part is 68

Step 2: Find the row in the log table for the first two digits of the number, which is 22. Then, look for the column in that row that matches the third digit, which is 6.

Step 3: For row 24 and column 6 in the log table, find the cell value at the intersection. The value here is 3909.

Step 4: Check the log table for the mean difference column corresponding to the fourth value of the given number, which is 8.

Step 5: The mean difference column for 8 for row 22 gives the value of 14.

Step 6: Combine the values found in Step 3 and Step 5. The value will be 3909 + 14 = 3923. It is the mantissa part of the value.

Step 7: Find the characteristic part for the value.

Characteristic part = (Number of digits to the left of decimal) - 1

So, the characteristic of the value will be 2-1 = 1

Step 8: Combine the characteristic part and the mantissa part to get a value. In this case, the value becomes 1.3923. So, we can write, log 24.68 = 1.3923

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Using Log Table for Natural Logarithm

There are separate sets of log values for a number for common logarithm (base 10) and natural logarithm (base e). To get the natural log value of a number using a common log table, we use the following formula:

log e x = log x/log e = log x/ log 2.718

For example: What is the value of ln 6?

ln 6 = log 6/log 2.718 = 0.7781/0.4343 = 1.7916 (approx.)

Important Notes on Log Table

• A log table is applicable for finding the logarithm of a number where the number of digits after its first non-zero digit is less than or equal to 4.
• If the number of digits is more than 4, we can ignore the digits from the 5 th digit onwards to find the log value.
• The log of a number has two parts: characteristic and mantissa and their combination is the logarithm value.
• The characteristic can be either positive or negative.
• The mantissa part is always positive.
• To find the logarithm of a base other than 10, we use the change of base of rule. For example, we can calculate log b = (log a) / (log b) and then use the values from the common logs table.

Log Table Solved Example

#1. Find the value of log (16.35)

Solution:

To find the common logarithm of the number 1.635, we need to first evaluate the mantissa part.

From the table, the intersection of rows corresponding to 16 (the first two digits) and column 3 (the third digit) of the table gives the value 2122.

Then, to find the mean difference, we check the value of column 5 (fourth digit) for the same row and column, which shows the value of 13.

So, the mantissa part is: 2122 + 13 = 2135.

To find the characteristic, the characteristic is the number of digits to the left of the decimal point minus 1, which means 1.

Here, there is only one digit to the left of the decimal point, so the characteristic is 0.

So, Log 1.635 = 0 + 0.2135 = 0.2135

This article discusses in detail the features and application of log tables for making complex calculations easy and efficient. Log tables simplify difficult computations, saving time and eliminating chances of errors. Join Online Tuition Class for Kids Now !!