# Explain like I'm 5: Logarithm

Once and for all, I learned what Logarithm is.

Posted on December 27, 2023Merry Christmas! Heading to the end of the year, thanks to the break we have, I decided to go all-in on a Data Structures and Algorithms course, to finally get a solid understanding of it, without breaks as I usually did in the past, because of work, other studies and etc.

One of the major things you learn to analyze on DSA classes is
the **Big-O Notation**, which is like a abstract and input-driven
way to express the time and space costs of executing an algorithm.
One of the common Big-O complexities is ** O(log n)** and

**, which are logarithmic complexities.**

`O(n log n)`

I have a superficial understanding of what a Logarithm is, but not enough to observe a piece of code and assert that the time complexity of it is in the realm of logarithmic time or space.

So, by searching, I found a pretty easy and simple definition:

The logarithm of b on base a is x if, and only if, a to the power of x is equals to b. log a b = x <=> a^x = b a -> base b -> logaritmand x -> logarithm

The essence of learning logarithm only for purposes of Big-O analysis is, you donâ€™t need to calculate the value of it, because it works based on the input, and we drop the constants while defining it. Remember: Big-O always respects input growth only.