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Log Values From 1 to 10

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Last updated date: 19th Mar 2024
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What are Log values?

In Mathematics, the logarithm is the most convenient way to express large numbers. The definition of the logarithm can be stated as the power to which any number must be raised to obtain some values. Logarithms are also said to be the inverse process of exponentiation. In this article; we will study Logarithm functions, properties of logarithmic functions, log value table, the log values from 1 to 10 for log base 10 as well as the log values from 1 to 10 for log base e.


Log values are important in mathematics and other related subjects such as physics. Students need to refer to the log values for finding different sums related to logarithms. The value of log 1 to the base 10 is given zero. The log values can be determined by using the logarithm function. There are different types of logarithmic functions. Log functions are useful for finding lengthy calculations and saving time. Using a logarithm function also makes it easier to solve a complex problem. By using logarithm functions students can reduce the operations from multiplication to addition and division to subtraction. Read here to know more about logarithm functions. 


Logarithms Function

The logarithm function is defined as an inverse function of exponentiation.

Logarithms function is given by

F(x) = loga x

Here, the base of the logarithm is a. It can be read as a log base of x. The most commonly used logarithm functions are base 10 and base e.

 

Rules for Logarithm

There are some rules of logarithm and students must know these rules to solve questions. The rules are given here:

  • Common Logarithms Function-

The logarithm function with base 10 is known as Common Logarithms Function. It is expressed as log10.

F(x) =log10 x


  • Natural Logarithms Function -

The logarithm function with base e is known as Natural Logarithms Function. It is expressed as loge.

F(x) =loge x


  • Product Rule

In the product rule, two numbers will be multiplied with the same base and then the exponents will be added.

Logb MN = Logb M + Logb N


  • Quotient Rule

In the quotient rule, two numbers will be divided with the same base and then the exponents will be subtracted, Logb M/N = Logb M - Logb N 


  • Power Rule

In the power rule, exponents' expressions are raised to power and then the exponents are multiplied.

Logb Mp = P logb M


  • Zero Exponent Rules

Loga = 1


  • Change of Base Rule

Logb (x) = in x/ In b or logb (x) = log10 x / log10 bValue of Log 1 to log 10 for Log Base 10 Table


Log Table 1 to 10 for Log Base 10

Common log to a number (log10X)

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


Here, we will list the log values from 1 to 10 for loge e in tabular format.


Log Table 1 to 10 for Log Base e

Common Logarithm to a Number (loge x)

Ln Value

ln (1)

0

ln (2)

0.693147

ln (3)

1.098612

ln (4)

1.386294

ln (5)

1.609438

ln (6)

1.791759

ln (7)

1.94591

ln (8)

2.079442

ln (9)

2.197225

ln (10)

2.302585


How to find the value of Log 1?

According to the definition of logarithm function, logan=x can be written as an exponential function:

Then ax = b

When the value of log 1 is not given, you can take the base as 10. Thus, you can express it as log 1 as log10 1.


Now, according to the definition of logarithm, we know the value of a =10 and b =1. Thus,

Log 10 x = 1

We can also write this as:

10x= 1


We already know that anything raised to the power 0 is equal to 1. Thus, 10 raised to the power 0 will tell that the above given expression is true. 

So, 100= 1

This is the general condition for the base value of log and the base raised to the power zero will give you the value of 1. 


This proves that the value of log 1 is 0. 

 

Alternative method to find log 1 or log to the base e?

We can also find the log value of 1

Log (b) = loge (b)

Thus,  Ln(1) = loge(1)

Or ex = 1

∴ e0 = 1

Hence, Ln(1) = loge(1) = 0

 

Important points to remember

  • Students must remember a few important points related to the logarithms. Some important points to remember are:

  • India was the first country in the 2nd century BC to use logarithm

  • Logarithm was first used in contemporary times by a German mathematician named Michael Stifel.

  • The inverse process of logarithms is also known as exponentiation

  • If one has to do theoretical work, natural logs are the best. They are easy to figure out quantitatively.

  • The most important advantage of using base 10 logarithms is that they are easy to calculate mentally for some numbers. For example, the log base 10 of 1,00,000 is 5 and you only have to count the zeroes. 


Solved Examples

  1. Solve the Following for the Value of x for log3 x = log34 + log37 by using the Properties of a Logarithm?

Solution: log3x = log34 + log37

= log34 + log37 = log3 (4 x 7) (by using the addition rule)

= log3(28)

Hence, x = 28


  1. Evaluate: log1 – log 0

Solution: log1 – log 0 (Given)

Value of Log 1 = 0 and Value of log 0 = - ∞

Hence, log 1+ log 0 = 0-(-∞) = ∞


  1. Find the value of log2(64)

Solution: x =64 (Given)

By using the base formula,

Log2 x = log10 x/ log10 2

= log2 64 = log10 64/ log10 2

=1.806180/ 0.301030= 6


Quiz Time

1. Logarithm Functions are the Inverse Exponential of

a. Verses

b. Functions

c. Numbers

d. Figures


2. How will you write the Equation 53= 125 in log form

a. Log 3 (125) =5

b. Log 125 (5) = 3

c. Log 5 (125) = 3

d. Log 5 (3 = 124)


3. What will be the value of log 9, if log 27 = 1.431?

a. 0.934

b. 0.945

c. 0.954

d. 0.958

FAQs on Log Values From 1 to 10

1. What is a Log Value Table and how to use it?

The log value table is used to compute the values of logarithmic functions. The easiest method to find the values of given logarithm functions is to use the log table.

Method to use Log Table

Step 1. Clearly understand the concepts of logarithms. The log table can only be used with a certain base. Log base 10 is the most common type of log table which is widely used.

Step 2. Recognize the characteristics and mantissa part for a given number. For example- if you want to find the value of log10 (15.27). Here in this, the characteristics part will be 15 whereas the mantissa part will be 27.

Step 3.  Now use the log table, Check the row number 15 and check the column number 2 to find their corresponding values. So the value will be 1818.

Step 4. Use the mean difference column in the log table, check the value of column 7, and row number 15 and mention their corresponding value as 20.

Step 5. Now add the value obtained in step 3 and 4. Values are 1818 + 20 = 1838.

Hence, the value of 1838 is the mantissa part.

Step 6. Now find the characteristic part. As the number lies between 10 and 100, ( 101 and 102. Here the characteristic part will be 1.

Step 7. Now combine both the values of characteristics and mantissa part. It will become 1.1838

2. Explain the Applications of Logarithm?

The concept of logarithm was first introduced by John Napier Later it was widely used by many scientists, navigators, engineers, etc for performing multiple calculations easily. The concept of the logarithm is also widely used in the field of Science and technology. Through the logarithm calculator, the problems based on logarithm will be calculated easily. The logarithm is also used in surveying and celestial navigation purposes. The logarithm is also used in calculations such as measuring the soundness, the intensity of the earthquake richter scale, in radioactivity decay to know the acidity (pH =- log 10 (H+)), etc

Hence, logarithm plays an important role in today’s life.

3. What are the two different types of logarithmic functions?

The two different types of logarithmic functions are described below:

The base of any common logarithmic function is 10. You can represent the function by log10 or log.

The base of the natural logarithmic function is given by e. You can represent the function by letters ln or loge.

4. Briefly describe some applications of a logarithm

The theory of logarithm was given by John Napier. The same was used by many other engineers, scientists, and navigators for doing various calculations. The logarithm is used in the field of science and technology. Logarithm functions can be used for calculating large calculations by using a logarithm calculator. This is also useful for celestial and surveying purposes. The logarithm is also useful in computations such as finding the soundness of a building, the intensity of an earthquake and the acidity of radioactivity.


Thus, logarithm plays an important role in today’s world and it makes it easy for the engineers and scientists to do large calculations easily.