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anonymous

  • 5 years ago

12^11 = 2^x How can I use log to solve this problem?

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  1. asnaseer
    • 5 years ago
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    Sorry the site went down and I lost everything I typed. let me try again...

  2. anonymous
    • 5 years ago
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    Sad face. Thanks for the effort though

  3. asnaseer
    • 5 years ago
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    If you have:\[a^b=c^d\]Then you can take logs of both sides to get:\[\log(a^b)=\log(c^d)\]\[\therefore b\log(a)=d\log(c)\]You should be able to use this to solve your problem.

  4. asnaseer
    • 5 years ago
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    Let me know f you need more help and/or explanation.

  5. anonymous
    • 5 years ago
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    what does the 3 dots mean before blog?

  6. asnaseer
    • 5 years ago
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    \(\therefore\) mean "therefore"

  7. anonymous
    • 5 years ago
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    okay, let me see if i can get it now, just a sec

  8. anonymous
    • 5 years ago
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    is the answer 39.5 approximately?

  9. asnaseer
    • 5 years ago
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    perfect! - well done

  10. anonymous
    • 5 years ago
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    thanks, but i need to ask you something

  11. asnaseer
    • 5 years ago
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    go ahead...

  12. anonymous
    • 5 years ago
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    the original question is the product of 12^11 x 18^13 = 2^p x 3^q, and it wants me to find 4q - 3p, and all of the possible answers are integers.

  13. asnaseer
    • 5 years ago
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    ok - interesting problem - it me think a bit...

  14. asnaseer
    • 5 years ago
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    ok - I think the best approach is try and replace the 12 and 18 by their prime factors.\[12=2^2*3\]\[18=2*3^2\]

  15. asnaseer
    • 5 years ago
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    can you "see" how to solve it then?

  16. anonymous
    • 5 years ago
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    2^2 x 3 x 2 x 3^2 = 2^3 x 3^3! Then you multiply by 11 and 13 respectively and get p = 33 and q = 39, 4 x 39 - 3 x 33 = 57 which isnt a possible answer. :(, did i mess up somewhere?

  17. asnaseer
    • 5 years ago
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    not quite - let me take you through it step-by-step...

  18. anonymous
    • 5 years ago
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    thanks

  19. asnaseer
    • 5 years ago
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    \[12^{11}=(12)^{11}=(2^2*3)^{11}=2^{22}*3^{11}\]use same technique with 18 and then see what you get.

  20. asnaseer
    • 5 years ago
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    I used the rule:\[(x^a)^b=x^{ab}\]

  21. anonymous
    • 5 years ago
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    ohh, forgot about that; p = 35, q = 37? So the answer is... 43, and its a possible answer! Yay

  22. asnaseer
    • 5 years ago
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    well done - you are a fast learning!

  23. asnaseer
    • 5 years ago
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    *learner

  24. anonymous
    • 5 years ago
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    Thanks. You are a good teacher.

  25. asnaseer
    • 5 years ago
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    :) Thanks

  26. anonymous
    • 5 years ago
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    United Kingdom? What's it like there?

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