math

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6^(2log(x)) = 8

  • math -

    assuming logs base 10,

    2logx = log_6(8)
    logx = 1/2 log_6(8)
    x = √(10^(log_6(8))

    now log_6(8) = log6/log8. so

    x = √(10^log6)^(1/log8)
    = √(6^1/log8)
    = 6^(1/log64)

  • math -

    take log of both sides

    log [ 6^(2logx) ] = log8
    2logx (log6) = log8
    2logx = log8/log6
    log x^2= log8/log6

    x^2= 10^(log8/log6)
    x = √( 10^(log8/log6) ) = 3.804339012

    check using your calculator, it works

  • math - go with Reiny -

    Go with Reiny's answer. I messed up my log base conversion.

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