We’re here to break down the basics of this mystical beast and hopefully help you understand it better than your professor ever could (sorry, guys).

First off, let’s start with what logarithms actually are. In short, they’re a way to express exponents in reverse. Instead of writing 10^3 as the answer to “what number times itself three times equals 1000?”, we can write it as log10(1000) = 3.

Now, you might be wondering why anyone would want to do this. Well, for starters, it’s a lot easier to work with large numbers when they’re in log form. For example, let’s say we have the number 1,234,567,890. If we wanted to find out how many times 10 would fit into that number (i.e., what is the exponent of 10 needed to get that result?), it would take us a while to do so by hand. But if we convert it to log form using base 10, we can simply write log10(1234567890) = x and solve for x.

Another reason why logarithms are useful is because they allow us to compare numbers with vastly different orders of magnitude (i.e., the number of zeros between them). For example, let’s say we have two numbers: 1234567890 and 0.000000000000000000000000001. If we convert both of these to log form using base 10, we can see that they’re actually not too far apart:

log10(1234567890) = 9.10
log10(0.0000000000000000000000001) = -24.00

As you can see, the difference between these two numbers is only around 15 orders of magnitude (i.e., 9.10 (-24.00)). This makes it much easier to compare and manipulate them in calculations than if we had to deal with their original forms.

And the best part? They’re not as scary as they seem once you understand how they work. So go ahead and give them a try in your next math problem who knows, maybe you’ll even enjoy it!