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If logb(x)+logx(b)=20, find ((logb)(x)))^2 +((logx)(b)))^2?

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  1. logb(x) + logx(b) = 20

    (logb(x))^2 + (logx(b))^2 = 400 - 2(logb(x))(logx(b))

    logb(x) = (ln(x))/(ln(b)

    logx(b) = (ln(b)/(ln(x)

    (logb(x))(logx(b)) = 1

    (logb(x))^2 + (logx(b))^2 = 398

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