Question

Simplify the logarithm...

Answer 1

\[ \log_{2} 2\sqrt{2}\]

Answer 2

@terenzreignz

Answer 3

You again?!
LOL
Let's get to work, then XD

Answer 4

First, the key property of logarithms at work here...
\[\Large \log_b b^p = p\]
This is important.
Digest this equation... and let me know when you're ready to proceed.

Answer 5

haha I've been waiting for you, it seems you've been on vacation haha, I've been asking random people for help lol. okay.

Answer 6

So... are you ready?
You better have the equation ingrained in your head, sport :P

Answer 7

haha yes I am.

Answer 8

Now, can we write $$\Large 2\sqrt{2}$$
as a single power of 2?

Answer 9

....? what do you mean by that

Answer 10

I mean write it as 2 raised to something...

Incidentally, getting the square root is the same as raising to a certain exponent... do you know what that exponent is?

Answer 11

isn't the exponent unknown here? so a variable such as x?

Answer 12

Unknown to YOU, maybe? >:)

LOL Just kidding.
Unknown to you *for now*

But we will find out soon.


In the meantime, I asked you a question, but for the sake of ease, I'll repeat it:

Getting the square root of a number is the same as raising that number... to WHAT exponent?

Answer 13

2?

Answer 14

So... what you're saying is...
\[\Large x^2 = \sqrt x\]
That can't be right.. lol

Answer 15

haha no it isn't....? this kind of confusing..

Answer 16

it definitely isn't actually

Answer 17

Well, let me just tell you... after all, I'm not your cruel maths teacher :3

Getting the square root is the same as raising to the exponent \(\LARGE \frac12\).

Got it?

Answer 18

oooh yeah

Answer 19

So... recap:
\[\Large \log_2 2\sqrt 2 = \log_2 2\cdot2^{\frac12}\]
Now, what do you do to exponents when you multiply terms with the same base?
Recall the laws of exponents:
\[\Large a^m a^n = a^{m+n}\]
Use this fact to your advantage.

Answer 20

you find the common denominator and add?

Answer 21

common denominator of the exponents.

Answer 22

Whatever floats your boat. Just add the bloody exponents XD

Answer 23

my book says to simplify it in a manner sort of like this\[\log_{2}2\sqrt{2}=x\]

Answer 24

is that the same way you're simplifying it?

Answer 25

We've worked together so many times and you still don't trust me?

Come on... :/

Answer 26

I need your help too Teren sooo....

Answer 27

haha no I do!.... so what is are equation?

Answer 28

Im being patient.........

Answer 29

It's TJ, Dave, and I'm sure I can lend a hand over to your question while I'm helping out our mutual acquaintance here. Tag away ^_^

Anyway, @hello1213 I thought I told you to add the exponents? :P

Answer 30

okay but it's hard to visualize... haha I'm getting confused with this lol

Answer 31

\[\Large 2^1 \cdot 2^{\frac12 }=\color{red}?\]

Answer 32

okay so is that \[2^{1/2} \times 2^{1/2} = 2^{2/2}\]

Answer 33

lol what?
I don't recall there being two 1/2 's

Answer 34

well don't I have to change \[2^1 \to 2^{1/2}\]

Answer 35

so I can add the exponents..

Answer 36

All right, fine, just add the exponents in whatever manner suits you and tell me what you get lol

Answer 37

i get \[2^{2/2}\]

Answer 38

when I add the exponents..

Answer 39

that's your answer?
So, basically, you're saying\[\Large 1 + \frac12 = \frac22 \]?

Answer 40

yes

Answer 41

this part is so basic I think I forgot how to add those hahaha... did I add them wrong?

Answer 42

You think?
2/2 is just 1.
So basically what you're saying is...
\[\Large 1 + \frac12= \frac22 = 1\]
So.. adding one half to 1... results in 1...
means half is the same as zero?

I want to kill whomever taught you how to add fractions.

Answer 43

hahaha isn't 1+1/2= 1.5 actually

Answer 44

Yes... so how in the world did you get 2/2?

I am not amused :|

Answer 45

ohhh okay haha wow i really messed up there so it's 3/2?

Answer 46

I mean it is 3/2!

Answer 47

Yes. So now we get :
\[\Large \log_22\sqrt2 = \log_2 2\cdot 2^{\frac12}=\log_22^{\frac32}\]
I trust you can work it from here...

Answer 48

okay I like the way you do this more than my book actually! it seems like less steps! Thank you! so I get as a final answer\[\log_{2} 2\sqrt{2}= \frac{ 3 }{ 2 }\]

Answer 49

That is correct.

Answer 50

awesome! I may need help with other math related problems in a little bit if you're still available... I'll tag you anyways... Thanks again!

Answer 51

Maybe just one more.
Sleepy.