Logarithmic functions are a mathematical tool that can be used to solve problems in a variety of areas, including calculus and algebra. In this article, we’ll explore what logarithms are, what they are used for, and some examples of how they can be used. By the end of this article, you should have a good understanding of what logarithms are and how they work.
What is Logarithm function?
The logarithm function is a mathematical function that takes an input in the form of a base number (e.g. 10), and transforms it into a fractional value (). For example, if we wanted to calculate the logarithm of 100, we would use the following equation:
In other words, the logarithm function takes our original number (100) and multiplies it by base 2 (), which equals to 1.41421356.
Properties of Logarithm
Here are some other properties of logarithm:
- A logarithm is defined as the power (base 10) of a number raised to a certain amount. In other words, it’s the number that when multiplied by itself gives you the original number again.
- The base associated with a logarithm determines how many digits are included in its representation. The most common bases for logs are 2, 3, 5, 7, and 10.
- To find the absolute value of a logarithm, simply add its abs() parameter together all the way up to but not including negative infinity (e.g., -3). Then take the absolute value of that result (i.e., +Infinity).
Laws of Logarithm
There are four basic laws of logarithm that can help you solve problems more quickly and easily. The following is a summary of each law:
Product rule
The product rule states that if you know the base and exponent of a logarithm, then you can calculate the absolute value of any other logarithm. For example, if you know that a number is written in base 10 (that is, with 1 through 10 as its digits), and you also know that the logarithm to BASE 10 of that number is 2, then you can conclude that the corresponding logarithm to BASE 100 (which would have ten more digits) will be 3.
Division rule
The Division Rule states that the power of a logarithm is inversely proportional to its base. In other words, if the base is increased, the power will decrease.
This rule can be used to solve problems involving ratios and multiples. For example, if you want to divide two numbers using their logs (base 10 and 2), you would use the following equation:
ln(10) ÷ ln(2) = 1/10 ÷ ½
Power Rule
The power rule in law of logarithm states that, for any real number m and any rational exponent a, the logarithm of m with a given exponent a is equal to the exponents times their logs. For example, if you want to know what the logarithm of 100 is, you would use the power rule by looking at it as follows:
10^Log(100) = 0.10
Change of base rule
The change of base rule in law of logarithms states that when a number is expressed in terms of another number, the original number can be changed to any other number with the same base. For example, 3 could be expressed as 2x or 5x depending on which base is being used (i.e., 3 = 6 when using binary and 3 = 10 when using decimal).
Conclusion
In this article, we explained all about logarithms that you may have missed. These laws and properties of logarithms are of great importance in mathematics and it’s not surprising that most schools even teach them to the children before they start working out any problems related to arithmetic or algebra.
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