A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

what are the two values of x that satisfy log_x 2=log_3 X

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

    can someone help me

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

    Use the definition of the log like we did with the others here.

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

    \[2 = log_3x \iff\ ?\]

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

    x=3^(log_x2) idk....there are two xs and it's seems ambiguous....like, if i do 2=x^(log_3 X) then, it's just weird..

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm not sure there are 2 values for x that apply here though.

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

    Wait, where's the 2 x's

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

    I only see one.

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

    log_x 2=log_3 X

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh, that's different.

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

    But even so, the rule still applies.

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

    \[Let\ k = log_3 x \implies 3^k = x\] But that means that \[k = log_x 2 \implies x^k = 2\]

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

    So if we take the first equation and raise it to the power of k we have \[3^{kk} = x^k = 2\]

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

    i get your previous answer. But why are you raising them to the pwr k??

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So that I can set them equal.

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh~

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

    Because now we can take the ln of both side and have \[k^2(ln 3) = (ln 2)\]

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so k = ?

  18. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the sqroot of ln2/ln3. But how did you go from x^k=2 to ln2?

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

    I didn't. I went from \[3^{k^2} = 2 \implies k^2(ln\ 3) = (ln\ 2)\]

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

    oh, ok. got it.

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

    Also \[k = \pm \sqrt{(\frac{ln 2}{ln 3})}\] Which is where you get your two solutions from.

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

    Though you still have to solve for x.

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

    wait, so there's two values for x too?

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

    Yes, because there are 2 values for k, and k is related to x.

  25. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[k = log_3 x\] Remeber?

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

    haha right~

  27. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So \[x = 3^k\]

  28. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So the two values that satisfy that equation for x are?

  29. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3^sqroot ln3/ln2 and the other one is the same except it's the negative root of ln3/ln2. yes? (please say yes ^^:)

  30. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It's ln2/ln3, but otherwise yes.

  31. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    YAY <3

  32. 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.