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anonymous

  • one year ago

Solve for x. logx+log(x-15)=2

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  1. hartnn
    • one year ago
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    hello :) what did you try?? tried combining those 2 logs?

  2. anonymous
    • one year ago
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    I know what you have to do, however, I am not sure how to do it :(

  3. anonymous
    • one year ago
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    I don't know how to combine the logs

  4. hartnn
    • one year ago
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    \(\log A + \log B = \log AB \) so how about log x + log (x-15) ?

  5. anonymous
    • one year ago
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    is it 20?

  6. hartnn
    • one year ago
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    you're asking if x = 20 ? how did you do all the steps so fast! :O

  7. anonymous
    • one year ago
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    I've been working on this problem for a really long time and I wasn't sure if I was doing the steps right so I posted on here. I think the answer is 20...I don't know what else it could be :(

  8. hartnn
    • one year ago
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    oh great! you've tried some steps... can you post them here, we'll correct then if required.

  9. anonymous
    • one year ago
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    Oh boy... I don't know where to begin! I'll write the most recent steps I've tried...one moment

  10. anonymous
    • one year ago
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    I used the formula \[a=\log _{b}(b ^{a})\]

  11. anonymous
    • one year ago
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    \[2= \log _{10}(10^2)\]

  12. hartnn
    • one year ago
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    for the right side? so, \(2 = \log 10^2 \)

  13. hartnn
    • one year ago
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    but for the left side we will need the formula I posted :)

  14. hartnn
    • one year ago
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    \(\log x + \log(x-15) = \log x\times(x-15) \\= \log 10^2\)

  15. anonymous
    • one year ago
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    \[\log _{10}(x)+\log _{10}(x-15)=\log _{10}(10^2)\]

  16. hartnn
    • one year ago
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    good

  17. anonymous
    • one year ago
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    \[\log _{10}(x(x-15))=\log _{10}(10^2)\]

  18. hartnn
    • one year ago
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    you get how \(\Large \log x + \log (x-15) = \log [x\times (x-15)]\) basically just a log property

  19. anonymous
    • one year ago
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    and the answeres are x=20 and x=-5 but we cant have a negative log so it must be 20

  20. hartnn
    • one year ago
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    if log A = log B, then A = B what that says is that you can just cancel out log on both sides! so we have x(x-15) = 10^2 got this?

  21. anonymous
    • one year ago
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    yes I just skipped the last steps at the end because they were really small and by then I already figured out my answers :)

  22. hartnn
    • one year ago
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    oh you solved it completely. excellent! x =20 is correct :)

  23. anonymous
    • one year ago
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    Thanks @hartnn , I appreciate your time :)

  24. hartnn
    • one year ago
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    welcome ^_^ happy to help :)

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