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Math Help - Logarithms, Exponentials, Many questions!

  1. #1
    Newbie bickitrainer's Avatar
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    Logarithms, Exponentials, Many questions!

    I need help on these questions:

    Calculate the exact value of H if:

    logH = (log2^1/2) / log2

    Also, I scanned these that I don't understand:




    If you are having trouble reading these, please tell me.
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  2. #2
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    Quote Originally Posted by bickitrainer View Post
    I need help on these questions:

    Calculate the exact value of H if:

    logH = (log2^1/2) / log2

    Mr F says: If you read this thread:

    http://www.mathhelpforum.com/math-help/urgent-homework-help/60945-logarithm-help.html

    you will realise that log H = 1/2 => H = ..... This question is indentical to number 8 below.

    Also, I scanned these that I don't understand:




    If you are having trouble reading these, please tell me.
    ..
    Last edited by mr fantastic; November 22nd 2008 at 07:56 PM. Reason: Corrected an error due to misreading the question
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    ..
    I have time for the first scanned page:

    6. a) 10^{\log P} = 10^{2 + \log x} = 10^2 \, 10^{\log x} \Rightarrow P = 100 x.

    6. b) Use the fact that \log_A B = C \Rightarrow A^C = B.

    7. a) Linear therefore y = mx + c where y = \log P and x = \log t.

    7. b) See 6. a).

    8. Dealt with in post #2.

    9. \log_{10} 5^x = \log_{10} 2^{x + 4} \Rightarrow x \, \log_{10} 5 = (x + 4) \, \log_{10} 2 = x \, \log_{10} 2 + 4 \log_{10} 2.

    Now use algebra to re-arrange to make x the subject. Then use a calculator to get a final answer to the required accuracy.
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  4. #4
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    to #7:

    Probably I didn't understand the question but in my opinion you get:

    1. From the diagram:

    \log(P)=-\dfrac35\cdot \log(t) + 3

    2. Now the question asks to find a law connecting P and t

    Therefore:

    10^{\log(P)}=10^{-\frac35\cdot \log(t) + 3}

    P=1000\cdot t^{-\frac35}~\implies~P=\dfrac{1000}{\sqrt[5]{t^3}}
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