Logarithms and Inverses

What do I know about Logs?? And Inverses?? If I really think about it...nothing! XD
Naw, jk. But if I actually think about about it, I only know so little... so let's begin!!

Starting with the first part:

LOGS

Logarithms. Log for short! hehe, log... Here are some main point about Logs!

• Logs are exponents! Yup, basically nothing but exponents. Except, just mixed around to look more smarticles! Let's take a look at our example below! In example 1, we see '3 to third power is 9'. In its' log form however, we would say, 'the logarithm of 9 to the base of 3 is 2'.

• There are two kinds of Logs: Common Logs and Natural Logs! :D

• By defualt, log will always have a base of 10, it's just hidden! This is known as a Common Log, which is why when you type in log(100) in our calculators, you get 2 as a answer. Unless the base is specified like the example above, the base of log will always be 10.

• Natural Logs, on the other hand, are different. We see it as (ln) and (e). ln is the inverse of e and vice versa, tha'ts why they cancel out each other. IT'S THE LAW!! x]
  
  
  
  
  
  



• e is an irrational number, like pi!! e = 2.7828183 and so on!! Maybe I should remember e since Cynthia took pi...lol


• Fun Fact: the e symbol is called epsilon in Greek! ;D

Enough about Logs! Let's move on to Inverses!

INVERSES

Now onto inverses! No pun for this one, darn...

• When given a function, graphically, you can figure out how the inverse will look like by switching the inputs and outputs in the table of values. Let's look at this function! Notice the table and the graph: Now look how I switch the inputs and outputs! Now the graph looks like so: So grpahically we can easily find the inverse, but now to find the inverse algebraically!
  
• To find the inverse of a function algebraically, we need to 'solve' for it! Let's use the previous function as an example! Let's take a look: This is our answer, but to make sure, we apply this equation to see if it really is:If the final answer for both is x, then we got ourselves an inverse! Now we verify that the square root of x is the inverse of x^2: So this is our inverse! BUT!! After solving for the inverse, we then must check to see if the answer will be either #5, a function, or #6, a standard equation, from the second bullet.

• If the inverse of a function remains a function, then it is a One-To-One. To know if a function is one-to-one without graphing/solving for the inverse, you simply use the horizontal line test! (It's also not a function because there is two outputs for every input instead of one.) Now we know that the inverse of f(x)=x^2 is an equation, meaning not one-to-one.
• One other note about inverses, to find the domain and the range of the inverse, you just switch it with the origional one. Ex.; f(x) = x^2 D: (all real numbers) R: [0, all real numbers]

f(x) = root of x D: [0, all real numbers) R: (all real numbers)

Now the second part of the Blog!

What did I not get?

• Well, I don't get most of the classwork, but hopefully we'll go over it in class.
• I still have some doubts in logs, solving wise. It's those fractions! -___-
• I need to resist using the calculator when graphing logs too...
• Natural logs still seem confusing.
• Some terms confuse me, I may know what it is and all, but I don't remember what it's called.
• And probably what everyone else has trouble with.... lol....Logs...

Part three!

Now I'm off to comment on your blogs!!

Although I assum they have been answered by now... TT__TT

SUPER SUPER LATE Dx I gotta stop doing that...