Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

LaronJaxon

  • 2 years ago

What is the solution to the equation 1/sqrt 8= 4^(m - 3) ?

  • This Question is Closed
  1. zordoloom
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    m=9/4

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

    \[\large \frac{1}{\sqrt{8}}=4^{m-3}\]

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

    One nifty way of doing this is to try to express both sides of the equation as exponentials, ie, one base, one exponent... preferably with the same base. So, let's start with \[\frac{1}{\sqrt{8}}\] 8 is just 2³, so let's put it that way...\[\large \frac{1}{\sqrt{2^{3}}}\] And remember that taking the square root means raising something to the 1/2 power, so...\[\huge \frac{1}{\left( 2^3 \right)^{\frac{1}{2}}}\] Using laws of exponents, you get

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

    \[\huge \frac{1}{2^{\frac{3}{2}}}\]Now remember that \[\large a^{-n}=\frac{1}{a^n}\] So eventually, we're left with \[\huge \frac{1}{\sqrt{8}} = 2^{-\frac{3}{2}}\] Now on to the other side of the equation...

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

    \[\large 4^{m-3}\] But 4 = 2² So, we can write it as \[\huge (2^2)^{m-3}\] Again, using laws of exponents, it is just equal to \[\huge 2^{2(m-3)}=2^{2m - 6}\]

  6. terenzreignz
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So, your problem becomes... \[\huge 2^{-\frac{3}{2}}=2^{2m - 6}\] Which can only mean \[\large -\frac{3}{2}=2m - 6\]

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

    And the rest, is history :D

  8. malice
    • 2 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The answer is m=9/4 (just took the test and got it right)

  9. 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.