Question

I need to be able to solve these without a calculator if possible. f(x)=(log_2(x))/x^2
FIND: f(1/2), f(1), f(4). I have never done this before without a calculator so if you could show me the process, I would appreciate it. Thanks

Answer 1

Okay, so for f(1/2), how can you rewrite 1/2 as a power of 2?

Answer 2

I honestly have no idea

Answer 3

So, you can rewrite 1/2 as 2^-1. Now, you have log_2(2^-1)/(1/2)^2. What's log_2(2^-1)?

Answer 4

Okay that is pretty simple. I have never done this so most of it I probably won't be able to do.

Answer 5

so have you got the first one yet?

Answer 6

No. I don't know how to find the value of the log

Answer 7

so here's a rule for you:
\[\log_{a}a^b = b \]

Answer 8

based on that, what is
\[\log_{2} 2^{-1}\]

Answer 9

-1

Answer 10

right. So now we have \[f\left(\frac{1}{2}\right) =\frac{\log_{2}\left(2^{-1}\right)}{\left(\frac{1}{2}\right)^2}=-\frac{1}{\left(\frac{1}{4}\right)} = -4\]

Answer 11

okay, i got it. The answer is negative. Does that work for all of them or is there different rules?

Answer 12

no, lets try four. how do you rewrite 4 as a power of 2?

Answer 13

well yeah the rule works for all of them but it's not always negative

Answer 14

Right.

Answer 15

2^2

Answer 16

yep, so what's log_2(2^2)?

Answer 17

1/8

Answer 18

and f(1)=0

Answer 19

yeah dude, you got it

Answer 20

I have other log questions if you wouldnt mind helping me

Answer 21

sure shoot

Answer 22

Thank you

Answer 23

if log_a2=.36, log_a3=.56 and log_a=.83 fins an approximate value for each of the following
a) log_a8 b) log_a(5/9) c)log_a12 d)log_a((fouthrt(2)/12)

Answer 24

not fins find*

Answer 25

what's the last one? I think you might have mistyped log_a=.83

Answer 26

sorry log_a5=.83

Answer 27

okay. so are you familiar with the rule
\[\log a + \log b = \log ab\]?

Answer 28

I have seen it but I have never used it

Answer 29

okay. so based on that, what is log_a(2) + log_a(2) + log_a(2)?

Answer 30

if you just multiply all the two's together

Answer 31

*twos

Answer 32

log_a6

Answer 33

My mistake log_a8

Answer 34

yeah

Answer 35

so since we know log_a(2) = .36 and log_a(2)+log_a(2)+log_a(2) = log_a(8), what is the value of log_a(8)?

Answer 36

1.08

Answer 37

the second and fourth ones seem a little more complicated

Answer 38

yeah
it's the same deal for the second and fourth. another thing that might help is\[\log a -\log b = \log\left(\frac{a}{b}\right)\]

Answer 39

Okay, I figured out the first three but I am lost with the fourth root

Answer 40

would it be fourthroot(.36)-(.56+.83)=-1.3