Question

Evaluate, \(log_{2}~\frac{1}{64}\)

Answer 1

Possible answer choices,
−6
−32
6
32

Answer 2

@ganeshie8 @mathslover Can you guys help? Or busy, at the moment?

Answer 3

Write 64 in terms of 2^n

what will be n?

Answer 4

I really don't know this is the first question, were starting to learn about it today, and my teacher doesn't explain anything. :/

Answer 5

Okay so, tell me one thing. Can I write 64 as 2^6 ?

Answer 6

@Joel_the_boss learn a little bit logarithm then, at least simple properties

Answer 7

Yes you can , well I think :/

Answer 8

I will write 64 as \(\color{blue}{2 \times 2 \times 2 \times 2 \times 2 \times 2 }\)

And if I calculate for the terms in blue, I get, 64.

So, I can write 64 as : \(2^6\)

Yes?

Answer 9

so 1/64 can be written as 2^-6 as simple as that @mathslover nicely explained good work

Answer 10

Yes,

Answer 11

Okay Joel

So, we have : \(\log_2 \cfrac{1}{64} \) as \(\log_2 \cfrac{1}{2^6}\)

RIght?

Answer 12

Alright I see how you got that, know what to do? :/

Answer 13

Now, I can write \(\cfrac{1}{2^6} \) as \(2^{-6}\)

So, I have : \(\log_2 2^{-6} \)

Getting it?

Answer 14

ehh, kinda I see what your doing and understand nut this whole area is unknown to me. :(

Answer 15

What*

Answer 16

Then I guess, I will have to agree with what @ribhu suggested. Go through with some of the basics of Logarithm and then try to do this question.

Answer 17

Here is a link :

http://www.purplemath.com/modules/logrules.htm

Good Luck! :)

Answer 18

logarithm is same as exponent

Answer 19

Alright thanks both of you! Yourr some awesome people! @mathslover Thanks a lot.

@ribhu Thanks for the help! Nice to meet . :)

@ganeshie8 Come in early and steals the show. :P

Answer 20

\[\large \log_2 \frac{1}{64} = ?\]

is same as asking

\[\large \frac{1}{64} = 2^{?}\]

Answer 21

logs are fun, cant resist to answer your first q :)

Answer 22

OH! That's the same thing the @mathslover did but he he did step by step, can it always be done that easily? Any exceptions with other numbers or rules?

Answer 23

Haha! Ganeshie8 is a superstar of OpenStudy!

Although, listen carefully to what he is explaining as this is pretty good way to learn logarithm.

\(\log_a x = y\) then \(x = a^y\)

Answer 24

There are some exceptions I guess. You will learn them as soon as you progress with some online study material on Logarithms etc.

I'm afraid if I will refer to anything deep here, then you may get confused.

Answer 25

^

Answer 26

i think remembering that `logarithm` is exactly same as `exponential function` helps in smoothly learning logarithm properties

Answer 27

`correct`
:D

Answer 28

No its fine guys, thanks for all the help! :) Lol You guys are the reason I love OS, teach me more than the getting paid to teach.

@ganeshie8 Yes I see the similarities. Thanks a lot guys. Ill make sure to tag you three for help xD

Answer 29

\[logarithm ~= ~exponent\]

chant that couple of times ;)


if you're a visual learner like me, below is the best video on logs
https://www.khanacademy.org/math/algebra2/logarithms-tutorial/logarithm_basics/v/logarithms

Answer 30

ok solved it and got -6, was that right?

I simplified then expanded and after that multiplied. Was I right?

Answer 31

\[\huge\color{Red}{\checkmark}\]

Answer 32

ok thanks :D