Okay kiddo, so you know how we count with numbers like 1, 2, 3, 4, 5, and so on? Well, it turns out that some things in computers and math are easier to understand and work with if we use a different way of counting called binary.
Binary is a way of counting using only two numbers – 0 and 1. That's it! So instead of using all the numbers from 1 to 10, we just count 0, 1, and then start over again with 10, 11, and so on.
Now, let's talk about logarithms. A logarithm is a way to figure out what power you need to raise a certain number to in order to get another number.
For example, if we have the equation 2^3 = 8, we can say that the logarithm (base 2) of 8 is 3. Why? Because we raised 2 to the power of 3 to get 8.
So, what is a binary logarithm? It's just like a regular logarithm, but we use binary numbers instead of regular numbers.
For example, let's say we have the equation 2^10 = 1024. We can say that the binary logarithm (base 2) of 1024 is 10. Why? Because we raised 2 to the power of 10 to get 1024, and we were counting in binary (0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010).
So, binary logarithms help us figure out what power we need to raise 2 to in order to get a certain number when we're counting in binary. It's a way to make things easier when we're working with computers and math!