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Math Help - Finding X in the Exponent

  1. #1
    Member OnMyWayToBeAMathProffesor's Avatar
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    Post Finding X in the Exponent

    I am stuck on these three problems. I have to find out what x is. Any help would be greatly appreciated.

    1.06^x=4.1

    50e^{.035x}=200

    3+2e^{-x}=6

    Thank you!
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  2. #2
    Member FalconPUNCH!'s Avatar
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    Hmm...I'm not sure if this is right but I'd probably take the natural log of both sides.
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  3. #3
    Member OnMyWayToBeAMathProffesor's Avatar
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    reply to FalconPUNCH

    so i should divide \frac{ln{4.1}}{ln{1.06^x}} but that gives me 24.21609205, which could not be X. or did i do this wrong? same thing for the other problems?
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  4. #4
    Member FalconPUNCH!'s Avatar
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    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    so i should divide \frac{ln{4.1}}{ln{1.06^x}} but that gives me 24.21609205, which could not be X. or did i do this wrong? same thing for the other problems?
    No it should turn out to be

    ln1.06^x = ln4.1

    (x)ln1.06 = ln4.1 because of the power rule

     x = \frac {ln4.1}{ln1.06}

    and just use a calculator to solve that. Well it did come out to be the same answer. Idk because I'm not a helper, so you should ask someone else.
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  5. #5
    Member OnMyWayToBeAMathProffesor's Avatar
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    reply to FalconPUCNH

    i am sorry, i did not mean to type the X in the ln equation. i did \frac{ln{4.1}}{ln{1.06}} and got 24.21509205. Thanks for your help anyway.

    Anybody else know?
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  6. #6
    Member FalconPUNCH!'s Avatar
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    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    i am sorry, i did not mean to type the X in the ln equation. i did \frac{ln{4.1}}{ln{1.06}} and got 24.21509205. Thanks for your help anyway.

    Anybody else know?
    I checked and it seems to be the correct answer.
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  7. #7
    Member OnMyWayToBeAMathProffesor's Avatar
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    reply to FalconPUNCH

    so if X=24.21609205 than 1.06^{24.21609205} should equal 4.1 but actually equals 1.079758817.

    any ideas?
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  8. #8
    Member FalconPUNCH!'s Avatar
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    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    so if X=24.21609205 than 1.06^{24.21609205} should equal 4.1 but actually equals 1.079758817.

    any ideas?
    Really? I get approximately 4.1
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  9. #9
    Member OnMyWayToBeAMathProffesor's Avatar
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    Reply to FalconPUNCH

    o, i forgot to add the parenthesis. Thank you very much for all of your gracious help. Would i employ the same technique to find out the other 2,

    50e^{.035x}=200

    3+2e^{-x}=6

    Once again, many thanks.
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  10. #10
    Member FalconPUNCH!'s Avatar
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    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    o, i forgot to add the parenthesis. Thank you very much for all of your gracious help. Would i employ the same technique to find out the other 2,

    50e^{.035x}=200

    3+2e^{-x}=6

    Once again, many thanks.
    Yes it should work too. Just remember that  ln(e) = 1
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  11. #11
    Member OnMyWayToBeAMathProffesor's Avatar
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    thank you.
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