Log Values From 1 to 10

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

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

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

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