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Math Help - help with this please

  1. #1
    Junior Member
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    help with this please

    not sure what to do
    Attached Thumbnails Attached Thumbnails help with this please-input-002.jpg  
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, rj2001!

    Sove for x\!:\;\;\pi^{1-4x} \:=\:e^{5x}

    Take logs: . \ln\left(\pi^{1-4x}\right) \;=\;\ln\left(e^{5x}\right) \quad\Rightarrow\quad(1-4x)\ln(\pi) \;=\;5x\ln(e)

    Since \ln(e) = 1, we have: . \ln(\pi) - 4x\ln(\pi) \;=\;5x \quad\Rightarrow\quad 4x\ln(\pi) + 5x \;=\;\ln(\pi)

    Factor: . x\bigg[4\ln(\pi) + 5\bigg] \;=\;\ln(\pi)

    Therefore: . x \;=\;\frac{\ln(\pi)}{4\ln(\pi) + 5}

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