anonymous
  • anonymous
Expand the logarithm Quesition about placement - My question is do I need to add parenthesis to logarithm answers?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
My book has these all over the place so I'm not sure.
anonymous
  • anonymous
I think you should add parenthesis idk i might be wrong
jdoe0001
  • jdoe0001
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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
so then yes add the parenthesis?
jdoe0001
  • jdoe0001
\(\bf log_4(3xyz)^2\implies 2\left( log_43+log_4x+log_4y+log_4z \right) \\ \quad \\ 2log_43+2log_4x+2log_4y+2log_4z\)
anonymous
  • anonymous
okay you're confusing me you just wrote both down
jdoe0001
  • jdoe0001
hmmm nope, the last line is the parenthesized version, expanded
anonymous
  • anonymous
okay so I don't add parenthesis.
jdoe0001
  • jdoe0001
well.. distributing the "2" will be, expanding, thus
anonymous
  • anonymous
@jim_thompson5910
anonymous
  • anonymous
I'm confused now and idk what I'm doing
jim_thompson5910
  • jim_thompson5910
the first step is to pull down the exponent 2 using this rule \[\Large \log_{b}(x^y) = y*\log_b(x)\]
anonymous
  • anonymous
right
jim_thompson5910
  • jim_thompson5910
after you pulled down the 2, you will have \[\Large 2\log_{4}\left(3xyz\right)\]
jim_thompson5910
  • jim_thompson5910
then you'll use the rule log(x*y) = log(x) + log(y) to expand out log(3xyz)
anonymous
  • anonymous
yep
jim_thompson5910
  • jim_thompson5910
use the rule log(x*y) = log(x) + log(y) to get... \[\Large 2\log_{4}\left(3xyz\right)\] \[\Large 2[\log_{4}\left(3xyz\right)]\] \[\Large 2[\log_{4}(3)+\log_{4}(xyz)]\] \[\Large 2[\log_{4}(3)+\log_{4}(x)+\log_{4}(yz)]\] \[\Large 2[\log_{4}(3)+\log_{4}(x)+\log_{4}(y)+\log_{4}(z)]\]
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
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 \[\Large 2(\log_{4}(3)+\log_{4}(x)+\log_{4}(y)+\log_{4}(z))\]
anonymous
  • anonymous
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.
jim_thompson5910
  • jim_thompson5910
then go with 2(log4 3+log4 x+log4 y +log4 z)
anonymous
  • anonymous
my book has examples written like yours so i think that's why I was confused. Thank you for helping me
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
I'm glad I could help clear things up

Looking for something else?

Not the answer you are looking for? Search for more explanations.