Consider how many digits a number has. The number 100 is ten times larger than the number 10, yet it has only one additional digit. The number 1,000,000 is 100,000 times greater than the number 10, yet it only has five extra digits. The number of digits in a number rises in a logarithmic fashion. Thinking about numbers also demonstrates why logarithms may be valuable for data visualization. Can you picture having to write a million tally marks every time you typed the number 1,000,000? You’d be there for the entire week! However, the “place value system” we utilize allows us to write numbers down in a far more efficient manner. This article will go through logarithms, logarithm tables, numerous logarithm applications, and much more.
What are Logarithms?
Have you ever heard about logs? The logarithm of any given integer is divided into two distinct portions. The integral portion, also known as the entire part, is referred to as the characteristic, whereas the decimal part is referred to as the mantissa. While the characteristic may be determined through visual inspection, the mantissa must be calculated using logarithmic tables.
Instead of a simple computation, we may use the logarithm table to get the logarithm of an integer. Before calculating the logarithm of a number, we must first understand its characteristic and mantissa parts.
- Characteristic Part – The characteristic component is the entire part of a number. Any number larger than one is positive, and any number fewer than the number of digits to the left of the decimal point in a given number is negative.
- Mantissa Part – The mantissa portion is the decimal part of the logarithm number, which should always be positive. If the mantissa component has a negative value, it must be converted to a positive value.
Exponents are the inverse of logarithms. A logarithm (also known as logs) is a mathematical expression that answers the question, “How many times must one “base” number be multiplied by itself to generate another number?”
For example, how many times must a base of ten be multiplied by itself to yield 1,000? The solution is three (1,000 = 10*10*10). As a result, the logarithm base 10 of 1,000 is 3.
Let us see some examples to understand it more clearly.
- 2 to the power of 2 is equal to the number 4. Now, the logarithm of 4 to the base 2 is 2.
- 3 to the power of 2 is equal to 9. Now, the logarithm of 9 to base 2 is 3.
- 5 to the power of 2 is equal to 25. Now, the logarithm of 25 to the base 5 is 2.
The Swiss mathematician named Joost Bürgi published the first table based on the notion of linking geometric and arithmetic sequences in Prague in 1620. John Napier, a Scottish mathematician, reported his discovery of logarithms in 1614. A logarithm table is a table that is used to calculate the values of various logarithm functions. It is generally known as a log table.
Real-World Applications of Logarithms
- Logarithms have a wide range of applications in the field of solving exponential equations.
- Logarithms can be used to solve equations that would otherwise require a long time and effort to solve.
- In terms of practical applications, it is used to measure decibels, Richter scale, star brightness, and many other things.
- Many experiments in chemistry schools use logarithms, such as the measuring of acidity and alkalinity.
Visit Cuemath to learn more about logarithms and the logarithms table, as well as the history of the invention of these magnificent concepts in a fun and entertaining way.