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 as 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.

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.

Types of Logarithm Function

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

Logarithm Functions Properties

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 b

Value of Log 1 to log 10 for Log Base 10 Table

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

Value of Log 1 to log 10 for Log Base e Table

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

Solved Examples

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

Solution: log3 x = log34 + log37

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

= log3 (28)

Hence, x = 28

2. 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-(-∞) = ∞

3. 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

Fun Facts

Logarithm was initially used in India in the 2nd century BC

Logarithm was first used in modern times by German Mathematician Michael Stifel

The basic advantage of using Logarithms base 10 is that they are easy to compute mentally for some special values. For Example- Log base 10 of 1.000,000 is 6, just you have to count the number of zeros.

Natural logs are easier to use for theoretical work. They are easy to calculate numerically.

FAQ (Frequently Asked Questions)

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

A: 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?

A: 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.