Logarithms

Last Updated : 30 Dec, 2024

In mathematics, a logarithm is the inverse operation of exponentiation. It is defined as the power to which the base number must be raised to get the given number.

Logarithms serve as mathematical tools that help simplify complex calculations involving exponential relationships.

If you know that b^x= y (where b is the base, x is the exponent, and y is the result), it means that you have to raise “b” to the power “x” to obtain the result “y”, then by using logarithm we can say that the log of “y” to the base “b” is “x”.

This can be written as: log_⁡b(y) = x. And it is read as logarithm of “y” to the base “b”.

Example:

If 2³= 8, then, log⁡₂(8)=3

If 5¹= 5 then, log₅(5) = 1

Also, logarithm of 1 in any base is always 0 as a⁰ = 1 or log_a1 = 0(for a > 0).

Note : If the number is same as the base then the its log value will always be equal to one.

Logarithm For Beginners

Logarithm Practice Questions

Logarithm for Aptitude Preparation

Logarithms for Programmers

Logarithms – FAQs

What are Logarithms?

Logarithm is the inverse of exponential which is used to find out to what power a base must be raised to yield a particular value.

What are Different Types of Logarithms?

There are two types of Logarithms:

Common Logarithm (Base 10)

Natural logarithm (Base e)

What are Logarithms used for?

Logarithm is used to find the power a number must be raised to yield a particular result. It is useful in finding pH level, exponential growth or decay, etc.

What is the Characteristic and Mantissa in a Logarithm?

The integral component (whole number part) of a number’s logarithm is the characteristic. It represents the magnitude of the original number. while ,the mantissa is the decimal portion of a number’s logarithm. It gives the fine adjustment required to obtain the exact value of the logarithm.

What is the value of log_a0?

Logarithm does not take 0 and negative numbers as its input hence log_a0 is not defined.

What are the 7 Rules of Logarithms?

The 7 Rules of Logarithms include

Product Rule

Quotient Rule

Power Rule

Change of Base Rules

Zero Rule

Identity Rule

Negative Rule

These rules are used for simplifying logarithmic expressions.

What is Logarithmic Product Rule?

According to the product rule, the logarithm of a product is equal to the sum of the logarithms of the individual factors:

logₐ(xy) = logₐx + logₐy.

What is Log Rule for Change of Base?

According to change of base rule of log, log_a(b) = [log_c(b)]/[log_c(a)], where c is any positive real number.

What is the Relationship between Logarithms and Exponentials?

Logarithms and exponentials are inverse operations. A logarithm tells you the exponent needed to reach a certain number, while an exponential raises a base to an exponent.

Laws of Logarithms

ashutoshunfc

Improve

Article Tags :