A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

using the Law of Logarithms to expand the expression.. Please help!

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

    \[\log \left( \frac{ 10^{x} }{ x(x ^{2}+1)(x ^{4}+2) } \right)\]

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

    have you considered first using the quotient rule for log? \[\log(\frac{u}{v})=\log(u)-\log(v) \\ \]

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

    \[\log(uv)=\log(u)+\log(v) \text{ is another rule you can use after that } \\ \log(u^r)=rlog(u) \text{ is the power rule which can also be used here }\]

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

    \[\log10^{x}-logx (x ^{2}+1)+\log(x ^{4}+2)\]

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

    I think you forgot to distribute the minus sign

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

    \[xlog10-logx(x ^{2}+1)+\log(x ^{4}+2)\]

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

    but since the denominator is looks like multiplication wouldn't be a addition?

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

    \[\log(\frac{10^x}{x(x^2+1)(x^4+2)}) \\ \log(10^x)-\log(x(x^2+1)(x^4+2)) \\ \log(10^x)-[\log(x(x^2+1)(x^4+2)) ] \\ \log(10^x)-[\log(x(x^2+1))+\log(x^4+2)]] \\ \log(10^x)-\log(x(x^2+1))-\log(x^4+2) \]

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

    though could also expand the log(x(x^2+1)) part too

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

    ooh so the signs changed because of the minus sign before the brackets?

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

    yep that is called the distributive property

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

    oh ok.. sorry i suck on paying attention to small details.

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

    ok so could i expand more after log(x(x^2+1))−log(x^4+2)?

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

    the log(x(x^2+1)) could be expanded more

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

    notice x(x^2+1) is a product of x and (x^2+1)

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

    would i t be: Logx+log (x^2+1)

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

    yes and don't forget we also have a - sign in front of the log(x(x^2+1) so you have: \[\log(\frac{10^x}{x(x^2+1)(x^4+2)}) \\ \log(10^x)-\log(x(x^2+1)(x^4+2)) \\ \log(10^x)-[\log(x(x^2+1)(x^4+2)) ] \\ \log(10^x)-[\log(x(x^2+1))+\log(x^4+2)]] \\ \log(10^x)-\log(x(x^2+1))-\log(x^4+2) \\ \log(10^x)-[\log(x)+\log(x^2+1)]-\log(x^4+2)\]

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

    anyways yes log(10^x) =xlog(10) but assuming this is log base 10 you could also simplify the x log(10) more

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

    it will just become x right?

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

    right

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

    since log 10=1

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

    yes

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

    the result is: \[x-\log (x)-\log (x ^{2}+1)-\log (x ^{4}-2)\]

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

    ?

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

    well you change the sign between x^4 and 2 for some reason

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

    oh haha yeah.. oops

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

    \[\log(\frac{10^x}{x(x^2+1)(x^4+2)}) \\ \log(10^x)-\log(x(x^2+1)(x^4+2)) \\ \log(10^x)-[\log(x(x^2+1)(x^4+2)) ] \\ \log(10^x)-[\log(x(x^2+1))+\log(x^4+2)]] \\ \log(10^x)-\log(x(x^2+1))-\log(x^4+2) \\ \log(10^x)-[\log(x)+\log(x^2+1)]-\log(x^4+2) \\ x \log(10)-\log(x)-\log(x^2+1)-\log(x^4+2) \\ x(1)-\log(x)-\log(x^2+1)-\log(x^4+2) \\ x-\log(x)-\log(x^2+1)-\log(x^4+2)\] should be right if the log's are in base 10

  28. 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.