A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

How can I simplify this: log10(4)log10(2) Please help

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

    log(ab) = log a + log b so log 10(4) log 10(2) = (log10 + log4)(log 10+log2) log 10 = 1 (log10 + log4)(log 10+log2)=(1+log4)(1+log2)

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

    I dont get it. But the original expression was: \[Log _{16}(a)+Log _{4}(a)+Log _{2}(a)\]

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

    I was trying to change the log to a unique base. and I got: \[\log(a)=7Log(16)Log(4)Log(2)/(\log4Log2+Log16*Log2+Log16*Log4)\] I got stacked there

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

    are you asked to find log(a)?

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

    Im asked to find a

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

    i think the expression isn't complete Log16(a)+Log4(a)+Log2(a) it should be an equation or you can't find a

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

    Yeah I was thinking about that too. Ok thanks

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

    Sorry the expresion was: Log16(a)+Log4(a)+Log2(a) =7

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

    do you think the equation can be solved now?

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

    yes

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

    can you explain it to me. I tried really hard and I got no much further.

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

    log16a.4a.2a = 7 log(2^7)(a^3) = 7 7 equals to log 10^7 so log (2^7)(a^3) = log 10^7 (2^7)(a^3) = 10^7 a^3 = 10^7 / 2^7 = (10/2)^7 a^3 = 5^7 a = 5^(7/3)

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

    i got 2^7 from 16x4x2 16 is 2^4 and 4 is 2^2 therefore 16x4x2 = 2^7

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

    what do you mean by: Log16a.4a.2a = 7 \[Log(16a*4a*2a)\] Is 10 the base? How did you end up with that?

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

    yes , if the base isn't written, it means the base is 10. one of the identities of logarithm is loga + logb = log(ab)

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

    Remember the original expression has different bases. \[Log _{16}(a)+Log _{4}(a)+Log _{2}(a)=7\]

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

    oh sorry, i thought the 16 is inside the logarithm. so the base is 16, 4 and 2? wait a moment i'll try solve it again

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

    Ok no problem

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

    Thanks

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

    ok i got it 16 = 2^4 and 4\[a ^{c}\]= 2^2 so \[\log _{2^4}a + \log _{2^2}a + \log _{2}a = 7\] the identity of logarithm: \[\log _{a^b}c = (1/b)logc\] \[(1/4)\log _{2}a + (1/2)\log _{2}a + \log _{2}a = 7\] \[(7/4)\log _{2}a = 7\] \[\log _{2}a = (4/7) 7 = 4\] we know that if \[\log _{a}b = c \] then \[a ^{c}=b\] \[\log _{2}a = (4/7) 7 = 4\] therefore \[2^{4} = a\] a=16

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

    dont mind anything i type above the sentence " the identity of logarithm", it's typo

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

    yeah i was thinking about that. Let me check it out and try to understand it. Thanks dude

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

    you're welcome

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

    \[\log_{a ^{b}}x ^{y}=(y/b)\log_{a}x \] put 16 and 4 as a power of 2..and use the above log property. hope this would help

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

    yeah thanks. It is clear now

  26. 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.