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Math Help - [SOLVED] Basic Logarithms

  1. #1
    Newbie adhiluhur's Avatar
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    Question [SOLVED] Basic Logarithms

    If  log_4(5)=-(3 over (2x)) , find the value of  log_0.04(8)=
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  2. #2
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    Hello, adhiluhur!

    I'm glad you solved it . . . Your problem is hard to read.


    \text{If }\log_4(5) \:=\:-\frac{3}{2x} .[1]

    . . \text{find the value of: }\:\log_{0.04}(8)

    We have: . \log_{0.04}(8) \:=\:P .[2]

    . . (0.04)^P \:=\:8 \quad\Rightarrow\quad \left(\frac{1}{25}\right)^P \:=\:8  \quad\Rightarrow\quad \left(\frac{1}{5^2}\right)^P \:=\:8

    . . \left(5^{-2}\right)^P \:=\:8 \quad\Rightarrow\quad 5^{-2P} \:=\:8


    Take logs, base 4: . \log_4\left(5^{-2P}\right) \:=\:\log_4(8)

    . . -2P\!\cdot\!\log_4(5) \:=\:\log_4\left(4^{\frac{3}{2}}\right) \quad\Rightarrow\quad -2P\!\cdot\!\log_4(5) \:=\:\frac{3}{2}


    Substitute [1]: . -2P\left(-\frac{3}{2x}\right) \:=\:\frac{3}{2} \quad\Rightarrow\quad P \:=\:\frac{x}{2} .[3]


    Equate [2] and [3]: . \log_{.004}(8) \;=\;\frac{x}{2}

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