Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

recon14193

  • 2 years ago

solve a log

  • This Question is Closed
  1. recon14193
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\log_{a}x+\log_{a}x-2=\log_{a}x+4 \]\ \[\log_{a}x(x-2)=\log_{a}x+4\] that is my work so far I do not know how to convert to exponential

  2. recon14193
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I am wondering if I divide by \[\log_{a}x+4\] and then have it equal to zero which means my final answer is just 1

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

    assuming the right hand side is \(\log_a(x+4)\) then your last job is to solve \[x(x-2)=x+4\]

  4. recon14193
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so the logs just drop out

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

    log is a "one to one function" so if \[\log(A)=\log(B)\] then \(A=B\)

  6. recon14193
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok I guess but I dont really understand

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

    ok suppose instead of log, you had \[f(x)=2x+4\]

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

    if you were told that \[2a+4=2b+4\] then you would know that \(a=b\) right?

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

    it is the same with the log if \(\log(x)=\log(y)\) then you know \(x=y\)

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

    in other words, as in your example, the only way for \(\log(x^2-2x)\) to be equal to \(\log(x+4)\) is if \(x^2-2x=x+4\)

  11. recon14193
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh I see now so if i understand correctly it is because we know they must be equal that the fact that it is a log of each does not matter because no matter what they yield the same result

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

    yes, exactly

  13. recon14193
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you I appreciate your help

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

    if i know \(\log(x)=\log(5)\) then i know that \(x=5\) i cannot be anything else

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

    yw

  16. 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