A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

help please Solve 64^x = 16^x−1. x = −2 x = −1 x = negative 1 over 4 x = negative 1 over 3

  • This Question is Closed
  1. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    HI!!

  2. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    since \[4^2=16\] and \[4^3=64\] this is the same as \[\huge4^{3x}=4^{2(x-1)}\]

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

    |dw:1442080279656:dw|

  4. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now that the bases are the same, solve by solving \[3x=2(x-1)\] for \(x\)

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

    I'm confused

  6. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    me too

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

    i sent a drawing of the problem

  8. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the idea is this: if \[\huge b^{\spadesuit}=b^{\heartsuit}\] then \[\spadesuit =\heartsuit\] in other words, if the bases are the same, then so are the exponents

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

    but the bases are not the same

  10. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ik

  11. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that is why i made them the same did you look at the answer i wrote above? i arranged it so the bases were equal

  12. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wanna go slow?

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

    yes please

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

    looking for cheap & free medals

  15. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok your two bases are 64 and 16 right?

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

    yes

  17. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and they are not equal

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

    no they are not equal

  19. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but both 64 and 16 are powers of 4

  20. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    because \[4^2=16\\ 4^3=64\] right?

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

    yes that's correct

  22. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so...\[64^x=(4^3)^x=4^{3x}\] clear?

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

    yes clear

  24. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how about \[16^{x-1}\] can you do the same thing with that one, like i did with \(64^x\)?

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

    \[^{4^{2}}\]

  26. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well actually \[\huge (4^2)^{x-1}\]

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

    yes that's correct

  28. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    which is the same as \[\huge 4^{2(x-1)}\]

  29. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so now your equation looks like \[\huge 4^{3x}=4^{2(x-1)}\]and the bases are now the same

  30. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that means the exponents must also be the same, i.e. \[3x=2(x-1)\]

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

    so would the answer be -1?

  32. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no i don't think so

  33. misty1212
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can you solve \[3x=2(x-1)\]?

  34. 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.