The logarithm table in mathematics is used to calculate the value of a logarithmic function. Log tables are the easiest way to determine the value of a given logarithmic function. This section explains the definition and the procedure for using the logarithm tables.
Logarithm tables are historically a list of mantissa, or the decimal parts of exponents that make base 10-numbers. These numbers indicate that the logarithm, or the exponent that acts on base 10 to make 120, is 2.07918.
The following is a mathematical definition of the Logarithm table. It is used to calculate the value of the logarithmic functions. You can use the following formula to determine the value of the logarithmic function.log table.Learn mathematics BYJU’S is easy to find.
Logarithmic Function Definition
This section explains the logarithmic function in detail and the procedure for using the logarithm tables. Also, get Antilogarithm table here for reference.
The logarithmic function can be described as an inverse function of exponentiation. Here is the logarithmic function:
For x, a> 0, and a1,
y= loga x, if x = ay
The logarithmic function can then be written as follows:
f(x), = log ax
The most common bases used in logarithmic functions are base e and base 10. Log function with base 10 is also known as the common logarithmic functions. It is designated by log , or simply log.
f(x), = log 10
Log function to base e is also known as natural logarithmic functions and is denoted with loge.
f(x), = log x
Instead of using simple calculations to find the logarithm for a number, the logarithm table can be used instead. Before we can find the logarithm for a number, it is important to know the characteristics and mantissa parts of the number.
- Characteristic part – A whole number is known as the characteristic part. Any number with a characteristic greater than one is considered positive. It is also positive if it is less than the number to the left from the decimal point. If the number is lower than one, the characteristic of that number is negative. It is one more than what is to the right of it.
- Mantissa Part– The decimal portion of the logarithm number, also known as the mantissa fraction, should always be positive. Convert the negative mantissa value to a positive value if it is found.
How do you use the Log Table and pdf?
Below is the procedure to calculate the log value for a number by using the log table. The log table is first to be used. You can refer to the log table to locate the values.
Step 1Learn the concept of logarithm. Log tables can only be used with a specific base. Log base 10 is the most popular type of logarithm tables.
Step 2Identify the characteristic and mantissa parts of the given number. If you are looking for the log value, then this is an example.10(15.27), First separate the mantissa and characteristic parts.
Characteristic Part = 15.
Mantissa part = 27
Step 3: Create a common log table. Use row number 15, check column number 2, and then write the value. The result is 1818.
Step 4The logarithm table can be used with a mean different. You can slide your finger into the column 7 and row 15 of the mean difference, and then write the 20 equivalent value.
Step 5: Add the values from step 3 and 4 together. This is 1818+20=1838. The mantissa portion is therefore 1838.
Step 6: Identify the characteristic part. The number is between 10 and 100.1102The characteristic part of the aforementioned should be 1.
Step 7: Combine the mantissa and characteristic parts, it will become 1.1838
Here’s an example
This is a sample example of how to calculate the value for the logarithmic function by using the logarithm tables.
Find the value log 10 2.7272
Step 1: Characteristic Part = 2 and Mantissa Part= 872
Step 2: Next, check the column number 7 and row number 28. The result is then 4579.
Step 3: Determine the mean difference value of row number 28 or column 2. The row and column values are 3
Step 4: Add up the values from steps 2 and 3 to get 4582. This is the mantissa portion.
Step 5: Because the number of digits on the left side is 1 the characteristic part of the decimal portion is lower than 1. The characteristic part is therefore 0
Step 6: Combine the characteristic and mantissa parts. It will be 0.4582.
The log 2.872 value is therefore 0.4582.
Log Table:The logarithm in Mathematics is the inverse operation of exponentiation. This means that the logarithm for a number is the exponent to the base value. Logarithm is repeated multiplication in simple cases. You can use the following formula to find the value for a logarithmic function.log table.
Many students have difficulty using the website.Logarithm table. Embibe has provided the PDF log table along with the table definition on this page. We also provide detailed instructions on how to use the logarithm tables.
Log Table: Concept & Definition
Before we show you the logarithm table, from which you will obtain all the values of the table, let’s first understand the concept behind the logarithmic functions. Logarithmic function are the inverses exponential functions. The following is a definition of a log function:
|For x, b> 0, and b1,Logb x is logb f(x), if x = by|
Here, f(x), is the logarithm function for base ‘b. Base e and 10 are the most commonly used bases in log functions.
Common Logarithm [fx] = log10[x] : The logarithm to base 10, which is b = 10, is also known as the common logarithm and is used in many areas of Science and Engineering.
Natural Logarithm [f(x), = loge[x]: The natural logarithm uses the number e (2.718Its base is ). Because it is simpler than its base, it is widely used in Maths and Physics.
Binary Logarithm [f(x), = log2[x]: The binary logarithm is base 2, which is b = 2, and is often used in Computer Science.
What is the difference between Mantissa and Characteristic in a logarithmic function.
The integral part of a logarithm common is known as theCharacteristicThe fractional portion is known as themantissa.
Notice: The mantissa portion of the log of a number must always be positive.
The log of any number N will thus be in the following form:
|logN = (Characteristic)(Mantissa)|
N =Antilog (Mantissa), x 10.Characteristics