# Logarithm Formula

## Logarithm Formula

Logarithms are commonly employed in mathematical and scientific operations. It facilitates the solution of difficult problems with variable exponents. Many physics derivations are only conceivable because of the Logarithm Formula. A logarithm is the inverse of an exponential computation process. Logarithms are frequently used in Physics, Chemistry, Biology, Computer Science, and other fields. Students may even locate logarithmic calculators, which have greatly accelerated and simplified their calculations. These have several uses in surveying and celestial navigation. This article will help students comprehend the notion of the logarithm. Students will look at numerous Logarithm Formula in Mathematics, along with examples and applications.

Students must completely study each of the Logarithm Formula, as well as comprehend the definitions of all themes and subtopics. Understanding the fundamentals of the Logarithm Formula is critical for better preparation. The greatest method to comprehend the fundamental ideas of Mathematics is to solve questions. Students should start with the easier questions and work their way up to the more difficult ones. Before commencing their preparation for Mathematics, students must become acquainted with the Logarithm Formula. The  Logarithm Formula is required in order to devise a strategy for studying the Logarithm chapters.

## What is a Logarithm?

The logarithm is just another means of representing exponents, and it may be used to solve problems that cannot be solved with only exponents. It is not difficult to comprehend logarithms. To comprehend logarithms, remember that a logarithmic equation is simply another way of stating an exponential equation. The inverse versions of the logarithm and exponent are each other. The Logarithm Formula is explained on the Extramarks website. Initially, a mathematician called John Napier invented logarithms to simplify computations, and the notion was immediately embraced by other scientists, engineers, and others.

The Logarithm Formula is used in Mathematics to solve Logarithm problems. In primary school, students are taught several algebraic properties such as commutative, associative, and distributive. Logarithmic functions have five essential characteristics. Using the Logarithm Formula, they may describe the logarithm of a product as a sum of logarithms, the logarithm of the quotient as a difference of logarithms, and the logarithm of power as a product.

### Logarithms Rules

There are seven Logarithm rules that may be used to expand, shrink, and solve the Logarithm Formula.

• Product Rule
• Quotient Rule
• Power Rule
• Zero Rule
• A Base to a Power Rule
• A Base to a Logarithm Power Rule
• Identity Rule

## Logarithm Formulas

There are two types of logarithms: common logarithms (which are represented as “log” and have a base of 10 unless otherwise specified) and natural logarithms (which are written as “ln” and its base is always “e”). The Logarithm Formula provided here is for common logarithms. They are, however, all applicable to natural logarithms as well.

## Basic Logarithm Formula

The following are some examples of basic the Logarithm Formula:

• logb (mn) = logbm + logbm
• logb (mn)= logbm- logbn
• logb (xy)= ylogbx
• logbmn= lgbn1/m
• m logb(x) + n logb(y) = logb(xmyn)

Sometimes, but not always, it is feasible to simplify the process of adding logarithms. In general, adding logarithms with various bases does not allow for more word combinations. However, as will be demonstrated later, it is possible to combine logarithms with the same base into a single statement including the product of the parameters. In general, removing logarithms, like adding logarithms, does not allow for additional simplification. However, how to subtract logarithms will be detailed in the following section. A rule will be presented to convert a subtraction of logarithms into a combined single logarithm with the division of the inputs. Extramarks’ educators have compiled the  Logarithm Formula in which all the addition and subtraction rules are provided.

### Change of Base Formula

The Logarithm from a given base ‘n’ to base ‘d’ will be converted in the change of base formula.

lognm= logdmlogdn

### Solved Examples

Questions based on the Logarithm Formula must be solved. All forms of Logarithm Formula problems should be practised on a regular basis. Students are encouraged to utilise the Extramarks learning platform to find solutions to the Logarithm Formula problems. Extramarks provide solutions to help students understand how to use the Logarithm Formula correctly. It is vital to continue practising questions from all chapters of the Mathematics syllabus. Pure Mathematics emphasises the existence and uniqueness of solutions, whereas practical Mathematics emphasises the logical justification of methods for approaching solutions. The Logarithm Formula may be used to represent almost any physical, technological, or biological activity, including celestial motion, bridge construction, and neural connections.

Mathematics is an important subject for pupils both in school and after they graduate. Many professional paths and industries still require proficiency in Mathematics after high school and college. Students must master the topic in order to make their daily life simpler. They can only perform well on examinations and answer issues that need quick calculations if they have a good comprehension of the subject. To be admitted to most college courses including Engineering, Economics, Business, or Mathematics honours, students must have Mathematics as a mandatory subject in Class 12 and perhaps take an admission exam. It is an important topic that must be prioritised for competitive examinations.

### Logarithm Applications

The Logarithm Formula has many uses both inside and outside of Mathematics. Students may consider the following instances of how Logarithms are utilised in everyday life:

• They are used to calculate an earthquake’s magnitude.
• The Logarithm Formula is used to compute the decibel level of noise, such as the sound of a bell.
• In Chemistry, logarithms are used to calculate acidity or pH.
• They are used to compute the growth of money at a particular interest rate.
• The Logarithm formula is frequently used to determine the time required for anything to decay or develop exponentially, such as bacterial growth or radioactive decay.

### How Do You Use a Log Table?

The logarithm table is used in Mathematics to discover the value of the logarithmic function. The log table is the easiest approach to getting the value of a given logarithmic function.

The Extramarks website offers reference materials which facilitate access to a simple approach to learning Mathematics.

## 1. What are logarithms?

Exponents can also be expressed using logarithms. A logarithm is defined as the number of powers to which a number must be increased in order to obtain some other number. In other terms, it answers the question, “How many times is one number multiplied to produce the other number?” A number’s Logarithm Formula is written as logb x = y.

## 2. What are the two varieties of logarithms?

The two most prevalent logarithm types are

• Base 10 Logarithm (or Common Logarithm)
• Base e Logarithm (or Natural Logarithm)

## 3. How should one prepare for the Mathematics exam?

In order to earn higher scores on the Mathematics test, students must continue reading the chapters and completing as many practice problems as possible. Students must solve sample papers and examinations from previous years at regular intervals. It is recommended that students refer to Extramarks’ revision notes when revising the chapters.

## 4. What is the purpose of logarithms?

• The earthquake’s potency is calculated using the Logarithm Formula.
• To calculate the decibel level of noise, such as the sound of a bell, logarithms are used.
• The pH level is determined by logarithms in Chemistry.
• For a given rate of interest, monetary growth can be calculated using logarithms.
• In order to calculate the time required for an exponential decline or growth, logarithms are commonly used. For example, bacterial proliferation, radioactive decay, and so forth.