Help me solve this logarithm question

Discussion in 'Calculus' started by raanikeri, Dec 1, 2023.

  1. raanikeri

    raanikeri

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    upload_2023-12-1_20-55-7.png
    upload_2023-12-1_20-56-13.png


    I checked the answer and it says upload_2023-12-1_20-55-40.png

    upload_2023-12-1_20-56-45.png

    I don't really understand this.
    Can anyone explain this to me? I couldn't find any online videos to help me understand this either.

    I do know how to convert from index form to logarithmic form and simplify logarithmic expressions, solve some logarithmic equations. I don't get how to sketch the graph to find the answer in these 2 questions though.
     
    raanikeri, Dec 1, 2023
    #1
  2. raanikeri

    e.jane.aran

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    e.jane.aran, Dec 2, 2023
    #2
  3. raanikeri

    HallsofIvy

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    If you want a more "analytic" (non-"sketch") take the exponential of both sides:
    x= e^{5- x}= e^5e^{-x}
    Multiply both sides by e^x:
    xe^x= e^5.

    Apply the "Lambert W" function (defined as the inverse function to xe^x) to both sides:
    x= W(e^5).
     
    HallsofIvy, Dec 7, 2023
    #3
    e.jane.aran likes this.
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