Logarithm – Meaning, Definition, Types, Properties, Applications, and FAQs

# Logarithm – Meaning, Definition, Types, Properties, Applications, and FAQs

## Logarithm Meaning

A logarithm is a mathematical function that takes a number (the base) and an exponent and produces a result (the logarithm). The logarithm of a number is the power to which the base must be raised to produce the number. For example, the logarithm of 1000 is 3, because 1000 = 10^3.

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## Logarithm Definition

Logarithm is a mathematical function that is used to calculate the power to which a base number must be raised to produce a given number. It is denoted by the symbol ‘log’. The logarithm of a number is the inverse of the exponential function.

## Logarithm Examples for class 9, 10, and 11;

Logarithm is the inverse of exponential function. The logarithm of a number is the exponent to which a given base must be raised to produce the number.

Logarithm examples with base 10:

The logarithm of 1000 is 3, because 10 raised to the power of 3 is 1000.

The logarithm of 10 is 1, because 10 raised to the power of 1 is 10.

The logarithm of 0.1 is -2, because 10 raised to the power of -2 is 0.1.

Logarithm examples with base e:

The logarithm of e is 0, because e raised to the power of 0 is e.

The logarithm of 10 is 2.302585092994046, because e raised to the power of 2.302585092994046 is 10.

The logarithm of 1/e is -1.4142135623730951, because e raised to the power of -1.4142135623730951 is 1/e.

## Logarithmic Form

An equation in logarithmic form is written in the form

y = axb

In this equation, a and b are constants, and x is the variable. The logarithm of y is equal to the logarithm of axb.

## Exponential Form

An equation in exponential form is written in the form y = axb, where a and b are constants. In this equation, y is the exponential function, and x is the variable. The exponential function is a power function with base a.

## Common Logarithm:

The natural logarithm is the logarithm to the base e. The common logarithm is the logarithm to the base 10.

## Natural Logarithm:

The natural logarithm of a number is the inverse of the exponential function. The natural logarithm of a number is the power to which the base e must be raised to produce the number.

## Properties of Logarithm

The logarithm of a number is the inverse of the exponential function

The logarithm of a number is the power to which a base must be raised to produce the number

The logarithm of a number is a real number

The logarithm of a number is unique

The logarithm of a number is continuous

The logarithm of a number is monotonic

The logarithm of a number is a function

## Note for Logarithm Class 9

A logarithm is the power to which a base is raised to produce a given number.

The logarithm of a number is the inverse of the exponential function.

Logarithms are used to solve problems involving exponential equations.

## Applications of Logarithms

There are many applications of logarithms in mathematics and science. Some of these are detailed below.

Logarithmic scales are used in many scientific and engineering applications. For example, the Richter scale for measuring the magnitude of earthquakes is a logarithmic scale. This means that a difference of one point on the scale represents a tenfold increase in magnitude.

Logarithmic scales are also used to measure the intensity of sound, the brightness of light, and the pH level of liquids.

Logarithms are also used in calculus. In particular, they are used to calculate derivatives and to find the roots of equations.

Logarithms can also be used to solve problems in physics and chemistry. For example, they can be used to calculate the concentration of a substance in a solution or to find the equilibrium constant for a chemical reaction.

1. Simplify:

log 3 125

3

log 125