Question

HELP!!! :(
Which of the following is the simplified version of 1/2 log 3 x - 2 log 3 y + 4 log 3 z ??????

Answer 1

Are you familiar with any log rules?

Answer 2

some of them , yes . like the ones you showed me earlier . i just dont understand this problem .

Answer 3

They just want you to condense this as much as possible

Answer 4

i'm confused because all of the ansers (except one) have sqaure roots in them .

Answer 5

The rules we'll use are this...

\[\Large y\log_{b}(x) = \log_{b}(x^y)\]

\[\Large \log_{b}(x) + \log_{b}(y) = \log_{b}(xy)\]

\[\Large \log_{b}(x) - \log_{b}(y) = \log_{b}\left(\frac{x}{y}\right)\]

Answer 6

We'll also use the idea that \[\Large x^{\frac{1}{2}} = \sqrt{x}\]

Answer 7

1/2 log3(x) - 2log3(y) + 4log3(z)
is that how its supposed to be set up, with the 3 as the base?

Answer 8

that's one way you can write it

Answer 9

We have this \[\Large \frac{1}{2}\log_{3}(x)-2\log_{3}(y)+4\log_{3}(z)\]

What is the first step?

Answer 10

i want to say that the first step is taking the square root to get ./x - 2log3(y) + 4log3(z) but i dont think thats right .

Answer 11

close

Answer 12

\[\Large \frac{1}{2}\log_{3}(x)-2\log_{3}(y)+4\log_{3}(z)\]

\[\Large \log_{3}\left(x^{\frac{1}{2}}\right)-2\log_{3}(y)+4\log_{3}(z)\]

\[\Large \log_{3}\left(\sqrt{x}\right)-2\log_{3}(y)+4\log_{3}(z)\]

Answer 13

then what?

Answer 14

either way, log3 is going to be out front, right?
so would it be, log3 ./x.
can you add -2log3 and +4log3 to get 2log3 ? then combine x & y ?

Answer 15

Hopefully in step 2, you can see I used the idea that \[\Large y\log_{b}(x) = \log_{b}(x^y)\]

Answer 16

no you can't add the logs the way you're describing because the stuff in the inside is different

Answer 17

ohh. so... i'm lost again :/ math isnt my strong point :(

Answer 18

sry made a typo, but I fixed it

Answer 19

oh wait...one sec

Answer 20

okay. hmmm... is it log3 ./xz^4 over y^2 ?

Answer 21

sry, i write it out,but then I realized I made a typo (and I can't go back and fix it). So i have to erase and rewrite


\[\Large \log_{3}\left(\sqrt{x}\right)-2\log_{3}(y)+4\log_{3}(z)\]

\[\Large \log_{3}\left(\sqrt{x}\right)+4\log_{3}(z)-2\log_{3}(y)\]

\[\Large \log_{3}\left(\sqrt{x}\right)+\log_{3}(z^4)-2\log_{3}(y)\]

\[\Large \log_{3}\left(\sqrt{x}*z^4\right)-2\log_{3}(y)\]

\[\Large \log_{3}\left(z^4\sqrt{x}\right)-2\log_{3}(y)\]

Answer 22

YAY! so i got it right??? :D

Answer 23

yes, keep going to get...


\[\Large \log_{3}\left(z^4\sqrt{x}\right)-2\log_{3}(y)\]

\[\Large \log_{3}\left(z^4\sqrt{x}\right)-\log_{3}\left(y^2\right)\]

\[\Large \log_{3}\left(\frac{z^4\sqrt{x}}{y^2}\right)\]

Answer 24

sweet!! thank you!!!

Answer 25

sure thing