Is There a Way to Find Symbolic Roots?

General Usage
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1

I’m able to find a floating point approximation of the a second derivative, but I know the actual answer is log(a). Is there a way to find this symbolically?

using ModelingToolkit
using Roots 
p(t,a)=1/(1+a*exp((-t))) # let k=1
let ex = Differential(t)(p(t,a))
           func_ex = build_function(expand_derivatives(ex), t, a)
           @eval ∂tk(t,a) = ($func_ex)(t, a)
       end

let ex = Differential(t)(∂tk(t,a))
           func_ex = build_function(expand_derivatives(ex), t, a)
           @eval ∂∂tk(t,a) = ($func_ex)(t, a)      
       end 
find_zeros(∂∂tk,0,10)
2

I think @shashi created some AbstractAlgebra integration to handle this, but I’m not certain about the state of it.