Like many mathematical subjects, logarithms have properties that allow us to perform certain algebraic conversions as well as rewrite entire expressions. The purpose of logarithm properties is to simplify the resolution of difficult problems.

Before you can understand the logarithm properties you must be familiar with the concept. If you are unfamiliar with the concept of logarithm, click here and read the article where we explain you in detail about it.

## Basic logarithm properties

### Equivalence

The property states that:

### Logarithm of 1(one)

The property states that:

Let’s go to the demo:

very simple!

Which is true, because by the mathematical rule, any number raised to **0(zero)** will always be equal to **1**.

### Logarithm of a in the base a

The property states that:

Let’s go to the demo:

very simple!

Which is obviously true!

Now it’s your turn:

Based on the basic logarithm properties, find the value of **x** in the equations below:

## Operative logarithm properties

### Logarithm of Product

The property states that:

Let’s go to the demo:

### Logarithm of Quotient

The property states that:

Let’s go to the demo:

### Logarithm of Power

The property states that:

Let’s go to the demo:

Now it’s your turn:

Based on the operative logarithm properties, find the value of **x** in the equations below:

## Advanced logarithm properties

### Conversion to logarithm

The property states that:

Let’s go to the demo:

This is one of the most useful and interesting properties because it teaches us how to convert any number to a logarithmic representation. This allows us to solve many difficult expressions involving logarithms.

### Change of base

The property states that:

Let’s go to the demo:

This is also a very important logarithm property because it teaches us how to convert a logarithm from one base to another logarithm from any other base. This allows us to simplify and solve many difficult equations.

Now it’s your turn:

Based on the advanced logarithm properties, find the value of **x** in the equations below: