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Like exponents, logarithms have rules and laws that work the same way as the rules of exponents. It is important to note that the laws and rules of logarithms apply to logarithms of any base. However, the same base must be used throughout a calculation.

We can use laws and rules of logarithms to perform the following operations:

Changing logarithmic functions to exponential form.

Addition

Subtraction

Multiplication

Division

Expanding and condensing

Solving logarithmic equations.

Laws of logarithms

The logarithmic expressions can be written in different ways but under certain laws called laws of logarithms. These laws can be applied on any base, but during a calculation, the same base is used.
The four basic LAWS of logarithms include:

The Product Rule Law
The Quotient Rule Law
The Power Rule Law
Change of Base Rule Law

Although logarithms are taught in schools to simplify computation involving large numbers, they still have a significant role in our daily lives.

Here are some of these applications of logarithms:

We use logarithms to measure the acidity and alkalinity of chemical solutions.

Measurement of earthquake intensity is performed on the Richter scale using logarithms.

The level of noise is measured in dB (decibels) on a logarithmic scale.

Exponential processes such as the decay of ratio active isotopes, growth of bacteria, the spread of an epidemic in a population, and cooling of a dead body are analyzed using logarithms.

A logarithm is used to calculate the payment period of a loan.

In calculus, the logarithm is used to differentiate complex problems and determine the area under curves.



Watch the video to learn more about Logarithms.

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