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Math Help - Simplify the expression (log question)

  1. #1
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    Simplify the expression (log question)

    Simplify
    e^(x+lnx)

    Without using tables or calculators determine the following
    log5(0.04) (5 is the subscript of the log)

    Also, how would you express this in terms of a and b if
    a = ln 2 and b = ln 3?
    ln 2 \sqrt 2

    Thanks!
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  2. #2
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    New Delhi
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    Quote Originally Posted by Skizye View Post
    Simplify
    e^(x+lnx)

    Without using tables or calculators determine the following
    log5(0.04) (5 is the subscript of the log)

    Also, how would you express this in terms of a and b if
    a = ln 2 and b = ln 3?
    ln 2 \sqrt 2

    Thanks!
    1)
    hint
    use identity  e^{a+b} = e^a \cdot e^b \ and\  e^{\ln x}= x
    Spoiler:

     e^{x+ \ln x}=e^{x} \cdot e^{\ln x}=e^x \cdot x =x e^x

    2) log5(0.04)
    hint:
    0.04=1/25
    log(a/b)=log a -log b
     \log_{5}{1}=0 \quad \because 5^0=1
     \log_{5}{5}=1 \quad \because 5^1=5
    Spoiler:

    [tex] \log_{5}(0.04)=\log_{5}(\frac {1}{25})= \log_{5}{1}-\log_{5}{25}
    0-\log_{5}{(5^2)}=0-2 \log_{5}{5}=-2 \cdot 1 =-2
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