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how do you solve

Discussion in 'Mathematics' started by fudgesweets, Mar 3, 2011.

  1. fudgesweets

    fudgesweets New commenter

    8^(-x)=8
     
  2. fudgesweets

    fudgesweets New commenter

    oops I meant how do you solve 8^(-x)=x

    sorry
     
  3. googolplex

    googolplex Occasional commenter

    take logs
     
  4. googolplex

    googolplex Occasional commenter

    (in response to OP)
     
  5. fudgesweets

    fudgesweets New commenter

    tried that got

    -xln8=lnx

    ln8=-(lnx) / x

    where to go from here?...
     
  6. Graph y=8^(-x) and see where it crosses y=x
    I preferred your first question though!
     
  7. googolplex

    googolplex Occasional commenter

    Like I said, in response to OP.
     
  8. DM

    DM New commenter

    You are not going to be able to "solve" it. You can use numerical methods to find an approximate answer.
    The simplest way is to spot the solution lies between 0 and 1 (sign change) and then type either 0 or 1 or something inbetween into a calculator, press = and then type 8 ^ -ANS = and keep pressing = until the desired accuracy is obtained. This converges very slowly so a different method would be preferable.
     
  9. DM

    DM New commenter

    A better method might be to identify the root between 0 and 1 and use Newton Raphson.
    f(x) = x - 8^(-x)
    f'(x) = 1 + ln (8) * 8^(-x)
    Type 1 into calc and press =
    Type ANS - (ANS - 8^(-ANS))/(1 + ln(8) * 8^(-x)) =
    Press = about three more times.
    Done.

     
  10. DM

    DM New commenter

    Corrected a missing ANS.
     

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