loglogk

function log(k::BigInt)
    if k < 10
        println(0)
        return
    end
    p = Array{BigInt}(0)
    num = BigInt(10)
    ex = 1
    res = 0
    push!(p,num)
    while num*num <= k
        num *= num
        ex *= 2
        push!(p,num)
    end
    i = length(p)
    k = div(k,num)
    res += ex
    while k >= 10
        if p[i] <= k
            k = div(k,p[i])
            res += ex
        end
        i -= 1
        ex = div(ex,2)
    end
    println(res)
end

log(9*BigInt(10)^1000)