# Logarithms explained.

Before we understand how logarithms work, it is important to know how **exponents** work.

aᶜ=b (read as "a to the power of c equals b") is an exponent where a,b and c are numbers.

aᶜ=b just means that a multiplied by itself c amount of times is equal to b.

![2.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1620905270045/U_NTMp4Z6.png)

Here are some examples: 
- 2² basically means 2 multiplied by itself 2 times which is 4
- 2³ basically means 2 multiplied by itself 3 times which is 8

So on and so forth.
![3.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1620905357838/0shShpFYL.png)

> Logarithms are basically a way of representing exponents in a different format. 

Let me show you what I mean, both the formulas that you see below are equal.

![6.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1620905407910/CYfZUJifV.png)

logₐb = c is basically saying that "a to the power of c = b".

Dare I say, logarithms are exponents in disguise.


![4.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1620905444580/NYhrZTzmv.png)

Here's a small exercise for you, what is the value of c in the below equations?

I've put them in logarithmic and exponential notation to make it easy for you.

![5.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1620905460632/FgoLfNoU6.png)


Logarithms are used in all sorts of places, machine learning, computer science (time complexities)... you name it.


![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1620905489841/Qnr8Zc364.png)


![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1620905498375/1cwVXexqp.png)

They are also a bunch of logarithmic properties that we can use to our advantage, but that is something I'll discuss in another blog post.

![image.png](https://cdn.hashnode.com/res/hashnode/image/upload/v1620905504318/GJ5-Iqxuc.png)

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Peace out!