Log Table 1 to 10 Overview
Logarithms are one of the most important mathematical concepts that find application in various fields, including engineering, physics, and computer science. A logarithm is a mathematical function that helps in converting exponential expressions into simple arithmetic operations. Logarithmic tables are the tables that provide the values of logarithmic functions for different values of the input. In this article, we will discuss log table 1 to 10 in detail.
Introduction to Logarithms
Logarithms are an essential concept in mathematics that represent the power to which a given base must be raised to produce a given number. They are widely used in various fields, such as science, engineering, and finance. In this article, we will provide an introduction to logarithms, including their definition, properties, and applications.
Definition
A logarithm is a mathematical operation that measures the power to which a given base must be raised to produce a given number. Mathematically, the logarithm of a number x with respect to a base b is defined as:
Log b(x) = y
Where,
b is the base, x is the number, and y is the power to which the base must be raised to produce x.
Log Table 1 to 10
Logarithmic functions are a type of mathematical function that maps the input value to its logarithm with respect to a specific base. These functions are widely used in various fields such as engineering, physics, and finance. In this article, we will discuss the types of logarithmic functions.
1. Natural Logarithmic Function
The natural logarithmic function is defined as the logarithm of a number with base e, where e is a mathematical constant approximately equal to 2.71828. This function is denoted as ln(x), and it is the inverse function of the exponential function e^x. The natural logarithmic function has several important properties that make it useful in calculus and other branches of mathematics.
2. Common Logarithmic Function
The common logarithmic function is defined as the logarithm of a number with a base of 10. This function is denoted as log(x), and it is widely used in engineering, physics, and other fields that deal with large numbers. The common logarithmic function is also known as the base-10 logarithmic function.
3. Binary Logarithmic Function
The binary logarithmic function is defined as the logarithm of a number with base 2. This function is denoted as log2(x), and it is widely used in computer science and information theory. The binary logarithmic function is also known as the base-2 logarithmic function.
4. Exponential Logarithmic Function
The exponential logarithmic function is a special type of function that combines the properties of exponential and logarithmic functions. This function is defined as f(x) = e^(kx), where k is a constant. The exponential logarithmic function is useful in modelling certain physical phenomena, such as radioactive decay and population growth.
5. Hyperbolic Logarithmic Function
The hyperbolic logarithmic function is defined as the logarithm of a number with respect to a hyperbolic function. This function is denoted as ln(x+sqrt(x^2-1)), and it is useful in hyperbolic geometry and other branches of mathematics.
Log Table 1 to 10: Logarithmic Rules
Logarithmic rules are a set of mathematical rules that govern the manipulation of logarithmic expressions. These rules are essential in simplifying and solving logarithmic equations. In this article, we will discuss some of the most common logarithmic rules.
Rule 1: Logarithmic Power Rule
The logarithmic power rule states that the logarithm of a number raised to a power is equal to the product of the power and the logarithm of the number. This rule can be expressed as:
logb(x^n) = n logb(x)
Rule 2: Logarithmic Product Rule
The logarithmic product rule states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the individual numbers. This rule can be expressed as:
logb(xy) = logb(x) + logb(y)
Rule 3: Logarithmic Quotient Rule
The logarithmic quotient rule states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the individual numbers. This rule can be expressed as:
logb(x/y) = logb(x) - logb(y)
Rule 4: Change of Base Rule
The change of base rule states that the logarithm of a number in one base can be expressed in terms of the logarithm of the same number in another base. This rule can be expressed as:
Log c(x) = log b(x) / log b(c)
Where,
C, b and x are positive real numbers with b and c not equal to 1.
Rule 5: Logarithmic Property of Zero
The logarithmic property of zero states that the logarithm of 1 is equal to 0. This rule can be expressed as:
Log b (1) = 0
Rule 6: Logarithmic Property of One
The logarithmic property of one states that the logarithm of the base of a logarithmic function is equal to 1. This rule can be expressed as:
Log b (b) = 1
Value of Log 1 to 10 for Log Base 10
Here is a list of the values of log 1 to 10 (common logarithm- log10 x).
| Common Logarithm to a Number (log10 x) | Log Value |
| 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 |
Value of Log 1 to 10 for Log Base e
This table shows the value of log 1 to 10 in terms of the natural logarithm (Log e x).
| Natural 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 |
Things to Remember about Log Tables 1 to 10
When using a logarithm table for base 10, there are a few important things to keep in mind. Here are some things to remember about log tables 1 to 10:
- The logarithm of 1 is always 0, regardless of the base.
- The logarithm of a number between 1 and 10 will be a positive number.
- The logarithm of a number greater than 10 will be a number greater than 1.
- The logarithm of a number between 0 and 1 will be a negative number.
- When using a logarithm table, be sure to find the appropriate column for the first two digits of the number you are trying to find the logarithm for.
- Once you have found the appropriate column, read across to find the row that matches the third digit of the number.
- The number you read off the table is the logarithm of the number you started with.
- Remember that logarithms are not defined for negative numbers or zero.
- When using a logarithm table, be careful to pay attention to the number of digits you are using, as rounding errors can significantly affect the accuracy of your results.
- Logarithm tables can be a helpful tool for solving logarithmic equations or performing complex calculations, but it is important to understand the underlying principles and concepts involved to ensure accurate results.