A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Solve and check. 4^2x= 32^1/2 Can someone walk me through the steps? Thank you!! :)

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

    32 to the power of 1/2

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

    @mthompson440 are you trying to simplify both sides of the equation?

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

    I don't know..?

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

    32^1/2= 16

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

    Divide both sides by 16.

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

    \[\large4^{2x}=32^{1/2}\]\[\large (2^2)^{2x} = (2^5)^{1/2}\]\[\large 2^{4x} = 2^{5/2}\]\[\large 4x = \frac{5}{2}\]\[\large x=~?\]

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

    Ok.. But I don't understand how to solve it.

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

    @Jhannybean explained it

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

    Your goal is to make the same base so you can evaluate their powers.

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

    X= 5/8?

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

    incorrect

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

    32 = 2 * 2 * 2 * 2 * 2 4 = 2 * 2 Theres an exponent rule that states having the same base allows for you to evaluate powers. \[\large a^x = a^y \implies x=y\]

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

    Yes @calecea . That is correct.

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

    @Jhannybean i thought it was 1

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

    @mthompson440 I kind of get it. I mean it's half of 32, but it was just confusing it's it's the exponent, not like multiplication.

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

    \[4x=\frac{5}{2} \implies x = \frac{5}{2\cdot 4} = \frac{5}{8} \ne 1\]

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

    @jhannybean thank you!

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

    @Jhannybean Oh lol

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

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

    @mthompson440 32\(^{1/2}\) \(\ne\) 16

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

    How do you get the 1/2 up there like that?

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

    \[32^{1/2} =\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{4^2 \cdot 2} = 4\sqrt{2} \ne 16\]

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

    what do you mean, "up there like that?"

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

    like by the 32

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

    \[32^1/2\]

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

    `^{1/2}`

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

    nvm figured it out

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

    Have you learned exponential functions, @calecea ?

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

    example problem: \(\large 7^{5x+3} = 512\)

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

    Now try solving this one.

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

    I have no idea. Probably.

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

    Using our knowledge of log rules, we know that: \(\log (a)^b \implies b\log(a)\)

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

    Okay, let's try that one instead.

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

    \[\large \log(x) +\log(x+48)=2\]

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

    Let me know how far you've gotten with it.

  36. 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.