Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

animalsavior94

  • 3 years ago

write as logarithm of a single quantity: 1/3[4log5(x+1)-3log5(3-x)+6log5x]

  • This Question is Closed
  1. nowhereman
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So how far do you get?

  2. animalsavior94
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not at all because its so confusing

  3. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is this log base 5?

  4. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    actually it doesnt matter so lets just write log

  5. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and ignore the 1/3 out front we will deal with it last

  6. animalsavior94
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes its a base 5

  7. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    first use \[\log(a^n)=n\log(a)\] backwards. all the multipliers come inside the log as exponents

  8. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[4\log(x+1)=\log((x+1)^4)\] \[3\log(3-x)=\log((3-x)^3)\] \[6\log(x)=\log(x^6)\]

  9. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    giving \[\log((x+1)^4)-\log((3-x)^3)+\log(x^6)\]

  10. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now we use \[\log(a)-log(b)=log(\frac{a}{b})\]

  11. animalsavior94
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what happened to the 1/3 outside the []

  12. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i will deal with that last

  13. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    not done yet!

  14. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[log((x+1)^4)-\log((3-x)^3)=\log(\frac{(x+1)^4}{(3-x)^3})\]

  15. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now we use \[\log(a)+\log(b)=\log(ab)\]

  16. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\log(\frac{(x+1)^4}{(3-x)^3})+\log(x^6)=\log(\frac{x^6(x+1)^4}{(3-x)^3})\]

  17. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now for the 1/3 out front. take the cube root of all that stuff.

  18. satellite73
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the inner stuff i mean. the cube root of x^6 is x^2, and the cube root of (3-x)^3 is 3-x and so you get \[\log(\frac{x^2(x+1)^{\frac{4}{3}}}{3-x})\]

  19. animalsavior94
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wow that was a hard problem but thanks again:)

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

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.