Question

Expand the logarithm
Quesition about placement -


My question is do I need to add parenthesis to logarithm answers?

Answer 1

My book has these all over the place so I'm not sure.

Answer 2

I think you should add parenthesis
idk i might be wrong

Answer 3

the "2" is multiplying the logarithmic function, thus if the logarithm expands to the "sum" version, the "2" has to multiply the expanded logarithmic version then

Answer 4

so then yes add the parenthesis?

Answer 5

\(\bf log_4(3xyz)^2\implies 2\left( log_43+log_4x+log_4y+log_4z \right)
\\ \quad \\
2log_43+2log_4x+2log_4y+2log_4z\)

Answer 6

okay you're confusing me you just wrote both down

Answer 7

hmmm nope, the last line is the parenthesized version, expanded

Answer 8

okay so I don't add parenthesis.

Answer 9

well.. distributing the "2" will be, expanding, thus

Answer 10

@jim_thompson5910

Answer 11

I'm confused now and idk what I'm doing

Answer 12

the first step is to pull down the exponent 2 using this rule

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

Answer 13

right

Answer 14

after you pulled down the 2, you will have

\[\Large 2\log_{4}\left(3xyz\right)\]

Answer 15

then you'll use the rule log(x*y) = log(x) + log(y) to expand out log(3xyz)

Answer 16

yep

Answer 17

use the rule log(x*y) = log(x) + log(y) to get...

\[\Large 2\log_{4}\left(3xyz\right)\]

\[\Large 2[\log_{4}\left(3xyz\right)]\]

\[\Large 2[\log_{4}(3)+\log_{4}(xyz)]\]

\[\Large 2[\log_{4}(3)+\log_{4}(x)+\log_{4}(yz)]\]

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

Answer 18

I used the rule in the smallest pieces possible. So it's a bit more dragged out than it has to be. You can just go from log(3xyz) to log(3)+log(x)+log(y)+log(z) in one step really

Answer 19

anyways, the point is that 2 on the outside is being multiplied by each term inside. You can leave the 2 out there like it is, but make sure you have surrounding parenthesis around those log terms

don't write \[\Large 2\log_{4}(3)+\log_{4}(x)+\log_{4}(y)+\log_{4}(z)\]

instead write \[\Large 2[\log_{4}(3)+\log_{4}(x)+\log_{4}(y)+\log_{4}(z)]\]

or write \[\Large 2(\log_{4}(3)+\log_{4}(x)+\log_{4}(y)+\log_{4}(z))\]

Answer 20

yeah I have options to choose from and the parenthesis around the 3,x,y,and z isn't an option it's just
2log4 3+log4 x+log4 y +log4 z or
2(log4 3+log4 x+log4 y +log4 z) so I feel like I will just go w/ the parenthesis.

Answer 21

then go with 2(log4 3+log4 x+log4 y +log4 z)

Answer 22

my book has examples written like yours so i think that's why I was confused. Thank you for helping me

Answer 23

as for what jdoe0001 did, he simply used the distribution rule to multiply the '2' by each term inside

eg: 2*(x+y) = 2*x + 2*y

Answer 24

I'm glad I could help clear things up