Tangent is drawn at the point `(x_i ,y_i)` on the curve `y=f(x),` which intersects the x-axis at `(x_(i+1),0)` . Now, again a tangent is drawn at `(x_(i+1,)y_(i+1))` on the curve which intersect the x-axis at `(x_(i+2,)0)` and the process is repeated `n` times, i.e. `i=1,2,3dot,ndot` If `x_1,x_2,x_3,ddot,x_n` from an arithmetic progression with common difference equal to `(log)_2e` and curve passes through `(0,2)dot` Now if curve passes through the point `(-2, k),` then the value of `k` is____