Question

Can this one be simplified?

Answer 1

\[\log _{2}1/4\]

Answer 2

Yes : \(\log_2 (\frac{1}{2})^2\)

apply \(\log_b a^n = n \log_b a\)

So we have : \(2 log_2 (\frac{1}{2})\)

Answer 3

Can you tell me how you got this?

Answer 4

We have a property : log_b (a^n) = n log_b (a)

Answer 5

so we get : \(2 \log _2 (2^{-1})\) = \(-2 \log_2 (2)\) = -2

Do you know why?

Answer 6

I don't, I have tried reading my textbook and just need help

Answer 7

see : as i mentioned the property ... so I can write : 1/2 as 2^{-1}
right?

Answer 8

ok

Answer 9

Now : I had : \(2\log_2 (\frac{1}{2}) \) So I can write that as \(2\log_2 (2^{-1})\)

Right?

Answer 10

oh ok i see

Answer 11

So by using the property I get :
\[\large{-2\log_2(2)}\]
s log_a (a) is 1 so log_2(2) will be 1

hence \[\large{-2\log_2(2) = -2*1 = -2}\]

Answer 12

Did that help @Virgo91684 ?

Answer 13

so final answer is \[-2\log _{2}^{(2-1)}\] or just just -2?

Answer 14

I do kind of, I am writing this all down for notes

Answer 15

-2...