Back to basics A long time ago in a galaxy far, far away…. And guess what, databases have to deal with both situations! The concept The time complexity is used to see how long an algorithm will take for a given amount of data.

Writing and evaluating logarithms Video transcript Let's learn a little bit about the wonderful world of logarithms. So we already know how to take exponents. If I were to say 2 to the fourth power, what does that mean? Well that means 2 times 2 times 2 times 2.

But what if we think about things in another way. We know that we get to 16 when we raise 2 to some power but we want to know what that power is.

So for example, let's say that I start with 2, and I say I'm raising it to some power, what does that power have to be to get 16? Well we just figured that out. And this is what logarithms are fundamentally about, figuring out what power you have to raise to, to get another number.

Now the way that we would denote this with logarithm notation is we would say, log, base-- actually let me make it a little bit more colourful. Log, base I'll do this 2 in blue Log, base 2, of 16 is equal to what, or is equal in this case since we have the 'x' there, is equal to 'x'?

This and this are completely equivalent statements. This is saying "hey well if I take 2 to some 'x' power I get 16'.

So with that out of the way let's try more examples of evaluating logarithmic expressions. Let's say you had What would this evaluate to? Well this is a reminder, this evaluates to the power we have to raise 3 to, to get to So if you want to, you can set this to be equal to an 'x', and you can restate this equation as, 3 to the 'x' power, is equal to Why is a logarithm useful?

And you'll see that it has very interesting properties later on. But you didn't necessarily have to use algebra. To do it this way, to say that 'x' is the power you raise 3 to to get to 81, you had to use algebra here, while with just a straight up logarithmic expression, you didn't really have to use any algebra, we didn't have to say that it was equal to 'x', we could just say that this evaluates to the power I need to raise 3 to to get to The power I need to raise 3 to to get to Purplemath.

The logs rules work "backwards", so you can condense ("compress"?) strings of log expressions into one log with a complicated argument. To write this as a single logarithm we will have to replace two of them with their values or we will have to combine these logarithms into one.

With the variables in the arguments we will not be able to find the value of log(x), log(y) or log(z). So we will have to combine these logarithms into one somehow.

Introduction. One of the best ways to improve your reach as a data scientist is to write functions. Functions allow you to automate common tasks in a more . Note. Historically (until release ), Python’s built-in types have differed from user-defined types because it was not possible to use the built-in types as the basis for object-oriented inheritance.

Port Manteaux churns out silly new words when you feed it an idea or two. Enter a word (or two) above and you'll get back a bunch of portmanteaux created by jamming together words that are conceptually related to your inputs.. For example, enter "giraffe" and you'll get back words like "gazellephant" and "gorilldebeest".

Remember that a logarithm is just a power; it's a lumpy and long way of writing the power, but it's just a power, nonetheless. The expression " log 2 (9) " means "the power which, when put on 2, turns 2 into 9.".

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