Logarithm and its Application- Log Values from 1 to 10

Logarithm is one of the most crucial mathematical concepts, acting as an easy method of getting answers to simple questions. While it is a very easy and efficient concept, you need to know the basics to use it practically or in your studies. 

To better understand this simple concept, we have provided the Log table for reference and easy instructions regarding its usage.

You can also use a Logarithm table PDF with examples to understand greater ways of using it.

HISTORY AND USAGE OF LOGARITHM

Logarithm has become an integral part of life. John Napier was the pioneer to introduce the concept of Logarithm, which was later recognised and widely used for various purposes and professions like scientific inventions, navigation, engineering, etc. This method is used for performing multiple calculations simply and effectively.

The concept of the logarithm is also widely used in the field of Science and technology. The problems based on logarithm can be calculated easily with the aid of a logarithm calculator. The logarithm is also beneficial in surveying and celestial navigation endeavours. 

In calculations involving measurement of sound, the intensity of the earthquake in a Richter scale, in radioactivity decay to find out the acidity, the logarithm calculator is used.

German Mathematician Michael Stifel was the first person to use logarithm in modern times. The primary advantage of using logarithms base 10 is that they are simple and efficient to compute mentally for some special values. 

For example, Log base 10 of 1.000,000 is 6. This can be done by just counting the number of zeros. For theoretical work, Natural logs are preferable as they are easy. It is simple to calculate numerically. 

LOG VALUES

Logarithm is an important and easier method to convey large numbers. 

Dividing or multiplying large numbers can be replaced by adding or taking away Logarithms. It is the power to which a number should be raised or brought to obtain or get some value. Exponentiation and logarithms are the inverse methods of each other. To gain a basic idea of logarithm, the following are to be focused on:

  • Logarithm functions
  • The log value table
  • Properties of logarithmic functions
  • For log base 10,  values between 1 and 10 and log base e, the values between 1 and 10.

LOGARITHM FUNCTION

The function of logarithm is an inverse of the exponentiation function. Generally, Logarithm function is stated as F(x) = loga x.

As stated above, the base of the logarithm is a. This can also be read as a log base of x.  Base 10 and base e is the logarithm functions that are commonly used.

FUNCTIONS OF LOGARITHM AND ITS TYPES

  • Common Logarithm Function: If base 10 is found in a logarithm function, it is a common Logarithm function.  This can be stated as log 10.

F(x) =log10 x

  • Natural Logarithms Function: If base e is found in the logarithm function, it is stated to be the Natural Logarithm function. It is to be expressed as log e.

F(x) =loge x

PROPERTIES OF LOGARITHM FUNCTION

Logarithm
Logarithm

Product: In the Product rule of logarithm function, two numbers are multiplied with the same base, and the exponents are added.

  1. Quotient: In the Quotient rule of logarithm function, two given numbers are divided with the same base, and the exponents are subtracted. 
  2. Power: In the Power rule of logarithm function, exponents’ expression is brought to power, and the exponents are multiplied accordingly.
  3. Zero exponent: Loga = 1
  4. The Change of Base Rule.

The following table lists out log values from 1 to 10 for log 10 in a table.

Common Logarithm to a Number (log10 x) Log Values
Log 1 0
Log 2 0.3010
Log 3 0.4771
Log 4 0.6020
Log 5 0.6989
Log 6 0.7781
Log 7 0.8450
Log 8 0.9030
Log 9 0.9542
Log 10 1

The following table lists out log values from 1 to 10 for log e in a table.

Common logarithm to a Number (loge x) Ln Value
In (1) 0
In (2) 0.693147
In (3) 1.098612
In (4) 1.386294
In (5) 1.609438
In (6) 1.791759
In (7) 1.94591
In (8) 2.079442
In (9) 2.197225
In (10) 2.302585

LOG VALUE AND ITS APPLICATION

The log table is used to find and identify the value of functions of logarithm. But using the log table, the needed values of given functions of logarithm could be found easily. 

  • 1st Step: It is a must to grasp an understanding of the concepts and rules of logarithm. Only a specific base is used in the log table. Base 10  log table is  the commonly available log table.
  • 2nd Sep: For a given number, try to identify and recognise the Mantissa part and characteristics part. For example, to find out log 10 value  (15.27), the mantissa part is 27, and the characteristics part is 15 here.
  • 3rd Step: Utilise the log table. Look for row number of log 10, which we know is 15, and then look for the second column to get their equivalent values. The result value obtained is 1818.
  • 4th Step: Utilise the column of mean difference available in the table. That is, check the seventh column and find its value. Then, check the row number of log 10, which is 15 and then mention their equivalent value, which is 20.
  • 5th Step: Addition of the value that was the outcome of the third and fourth steps. Values obtained are 1818 and 20 = 1838.
  • 6th Step: Identify the characteristics part. The given number comes between 10 &  100. (101 and 102. so, the characteristics part is 1 here.
  • 7th Step: Combine the values obtained of the mantissa part and characteristics. The result will be 1.1838.

CONCLUSION

Logarithm can be a powerful tool if you know how to use it properly. So, take tips from here and get all the fundamentals of the topic down.

Read also: HOW TO PREPARE FOR THE CLASS 5 MATH OLYMPIAD

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