A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Expand the logarithm Quesition about placement - My question is do I need to add parenthesis to logarithm answers?

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I think you should add parenthesis idk i might be wrong

  3. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so then yes add the parenthesis?

  5. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay you're confusing me you just wrote both down

  7. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay so I don't add parenthesis.

  9. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @jim_thompson5910

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  12. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the first step is to pull down the exponent 2 using this rule \[\Large \log_{b}(x^y) = y*\log_b(x)\]

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    right

  14. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    after you pulled down the 2, you will have \[\Large 2\log_{4}\left(3xyz\right)\]

  15. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yep

  17. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    use the rule log(x*y) = log(x) + log(y) to get... \[\Large 2\log_{4}\left(3xyz\right)\] \[\Large 2[\log_{4}\left(3xyz\right)]\] \[\Large 2[\log_{4}(3)+\log_{4}(xyz)]\] \[\Large 2[\log_{4}(3)+\log_{4}(x)+\log_{4}(yz)]\] \[\Large 2[\log_{4}(3)+\log_{4}(x)+\log_{4}(y)+\log_{4}(z)]\]

  18. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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

  19. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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.

  21. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  23. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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

  24. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm glad I could help clear things up

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.