How to Use Log Tables for Fast Calculation in Maths
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
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
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-(-∞) = ∞
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 Logarithm Values From 1 to 10: Complete Table
1. What are the values of log 1 to 10?
The values of logarithm base 10 (log10) for integers 1 to 10 are as follows:
- $\log_{10} 1 = 0$
- $\log_{10} 2 \approx 0.3010$
- $\log_{10} 3 \approx 0.4771$
- $\log_{10} 4 \approx 0.6021$
- $\log_{10} 5 \approx 0.6990$
- $\log_{10} 6 \approx 0.7782$
- $\log_{10} 7 \approx 0.8451$
- $\log_{10} 8 \approx 0.9031$
- $\log_{10} 9 \approx 0.9542$
- $\log_{10} 10 = 1$
2. What is the value of log 2 to log 10?
The logarithmic values for base 10 from 2 to 10 are:
- $\log_{10} 2 \approx 0.3010$
- $\log_{10} 3 \approx 0.4771$
- $\log_{10} 4 \approx 0.6021$
- $\log_{10} 5 \approx 0.6990$
- $\log_{10} 6 \approx 0.7782$
- $\log_{10} 7 \approx 0.8451$
- $\log_{10} 8 \approx 0.9031$
- $\log_{10} 9 \approx 0.9542$
- $\log_{10} 10 = 1$
3. What is the value of Log10 0?
The logarithm of 0 to base 10, written as $\log_{10} 0$, is undefined. This is because there is no real number $x$ for which $10^x = 0$. In mathematical terms, logarithms are only defined for positive real numbers. For a thorough understanding of such fundamental concepts, Vedantu provides step-by-step explanations in its online classes.
4. How do you calculate log values?
To calculate logarithmic values (especially to base 10), you can:
- Use memorized values or logarithm tables for common numbers (like log 2, log 3, etc.)
- Apply logarithmic properties:
- $\log_{10} (a \times b) = \log_{10} a + \log_{10} b$
- $\log_{10} (a / b) = \log_{10} a - \log_{10} b$
- $\log_{10} (a^n) = n \cdot \log_{10} a$
- Use scientific calculators for direct computation
5. What is the use of log values from 1 to 10 in mathematics?
The logarithm values from 1 to 10 are widely used in mathematics to:
- Simplify complex multiplication and division into addition and subtraction
- Solve exponential and logarithmic equations
- Perform scientific calculations, especially in chemistry and physics
- Work with logarithmic scales, such as pH or Richter scale
6. Why is log 1 equal to zero?
The value of $\log_{10} 1$ is zero because $10^0 = 1$. In other words, the exponent to which 10 must be raised to yield 1 is 0. This property holds true for logarithms with any base: $\log_{a} 1 = 0$ for any positive $a \neq 1$. Vedantu’s comprehensive lessons help clarify such core concepts with illustrated examples and practice problems.
7. How can students memorize log values for quick calculations?
To memorize log values from 1 to 10, students can:
- Practice writing them repeatedly
- Use mnemonic techniques or story-based associations
- Create flashcards for regular revision
- Utilize charts and tables during study sessions
8. What is the difference between natural logarithm and common logarithm values?
The common logarithm has a base of 10 $(\log_{10}x)$, while the natural logarithm has a base $e$ (approximately 2.718), denoted as $\ln(x)$. Their values for the same number will be different because of the distinct bases. For example, $\log_{10} 2 \approx 0.3010$ but $\ln 2 \approx 0.6931$. On Vedantu, students can explore both types of logarithms with clear tutorials and real-life examples.
9. How are log tables useful for students in examinations?
Logarithm tables help students quickly find log values without complex calculations. During exams, especially those without calculators, log tables become invaluable for:
- Multiplying or dividing large numbers
- Finding square roots and exponents
- Solving logarithmic equations quickly
10. Where can students practice log values from 1 to 10 with solved examples?
Students can practice log values from 1 to 10 with a variety of solved examples and worksheets available through Vedantu’s online learning platform. These resources include step-by-step solutions, interactive exercises, and personalized feedback to help learners master logarithmic concepts and enhance their problem-solving skills.
