Question

evaluate log4 (1/32)

Answer 1

\[\Large \log_4\left(\frac{1}{32}\right)\]We gotta figure this out? Hmmm

Answer 2

I guess we could ummm do something like this,\[\Large \log_4\left(\frac{1}{32}\right)\quad=\quad \log_4\left(\frac{1}{16}\cdot\frac{1}{2}\right)\]And then using a rule of logs:\[\Large \color{teal}{\log(a\cdot b)\quad=\quad \log(a)+\log(b)}\]We can write it as:

Answer 3

\[\Large \log_4\left(\frac{1}{16}\cdot\frac{1}{2}\right)\quad=\quad \log_4\left(\frac{1}{16}\right)+\log_4\left(\frac{1}{2}\right)\]

Answer 4

Should be a little bit easier to work with from here.
\[\Large \frac{1}{16}\quad=\quad \frac{1}{4^2}\quad=\quad 4^{-2}\]Do you understand how we're able to write the 1/16 like this?

Answer 5

yes thnx!

Answer 6

The 1/2 is a little tricky :)\[\Large \frac{1}{2}\quad=\quad \frac{1}{\sqrt4}\quad=\quad \frac{1}{4^{1/2}}\quad=\quad 4^{-1/2}\]Do you understand how to solve the problem from there? :o

Answer 7

actually got confused there

Answer 8

heh :)

Answer 9

\[\Large 2\quad=\quad \sqrt4\]Ok with that part? :o

Answer 10

yes

Answer 11

Don't remember how to write roots as rational expressions? :)

Answer 12

kinda