Question

Can anyone explain logs to me?

Answer 1

Sure thing.
When a tree is cut down, either by sawing or uprooting, the resulting 'tree carcass', particularly its wooden trunk, is called a "log"

:3

Answer 2

Though seriously, is there anything in particular you don't get? ^_^

Answer 3

Lol thanks though but yes the whole thing lol

Answer 4

That's a bit of a pity :)
Are you in any sort of hurry?

Answer 5

Eh not really but the moved me out of my Algebra II class into a precollege course so I didnt get to learn alot of the things they thought I knew

Answer 6

Intriguing... so you're the really smart-type, huh?
We shall see about that >:)

Just kidding (sort of)

Let's start with basics.
Ever heard of "Inverse Functions" ?

Answer 7

No I am nowhere near as smart as they think haha! Anywho yes I have

Answer 8

Let me see for myself just how smart you are :)
The name's TJ (for Terence Jason)

Since this is going to be a bit of a lengthy discussion (I think?) we might as well get familiar.


And speaking of familiar, since you are...familiar... with inverse functions, I'm just going to skim through them, all right?

Now...

Answer 9

Well Hello TJ it is very nice to meet you and thank you so much for your help

Answer 10

The "inverse" of a function, simply put, is a function that reverses the effects of another function, mathematically put, the inverse \(\large f^{-1}\) of a function \(\large f\) has the properties:
\[\Large \left(f^{-1}\circ f\right)(x)=x = \left(f\circ f^{-1}\right)(x)\]


For example: If we let
\[\Large f(x) = 2x - 3\]
Then \[\Large f^{-1}(x)=\frac{x+3}{2}\]

Verify for yourself that these functions are inverses.

Ready to proceed to the real deal?

Answer 11

Wait a second so like if I have f(x)=5x+3 it would be f^-1(x)=x+3/5?

Answer 12

f(x)=5x-3*

Answer 13

Nice save. :P
So, are you ready to proceed to the next step? ^_^

Answer 14

Lol yes I think I understand that now

Answer 15

Just to be sure... if I have
\[\Large g(x) = x^2\]
Then...
\[\Large g^{-1}(x) = \color{red}? \]

Answer 16

g-1(x)=x? Because then you are taking away one of the exponents?

Answer 17

Nope.
Not even close ;)

Think on it without getting into the nitty-gritty of Maths stuff, g is the SQUARING function, so what function would REVERSE its effects?

Answer 18

x^-2?

Answer 19

I told you im not smart at all lol

Answer 20

Still no.

Let's try this tack:

I *square* 4 to get 16.
What do you do to 16 to get back 4?

Answer 21

divide it by 4

Answer 22

Or take the square root

Answer 23

Which is it?
There can only be one.

If I square 5, I get 25.
If I divide 25 by 4, do I get 5?

Answer 24

no so you would square root 16 to get 4 and

Answer 25

Heh...
Silly <insert-your-name-here-or-whatever-the-heck-you-want-to-be-called-because-I-haven't-the-slightest-idea>,

There, you finally understood it, the inverse of the squaring function is the square root function :)

\[\Large g(x) = x^2\]\[\Large g^{-1}(x)=\sqrt x = x^{\frac12}\]

Got it?

Answer 26

Yes

Answer 27

Oh?
Try this:
\[\Large h(x) = x^2 - 7\]\[\Large h^{-1}(x)=\color{red}?\]

Answer 28

Let me just apologise (only lightly though ;) ) for all this thoroughness, you'll have a hard time with logarithms without a solid footing in the concept of inverse functions.

Just saying ^^

Answer 29

Hey sorry I jumped off my teacher wrote me up for being online and getting help instead of "asking" for it since I dont understand