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I think Right answer is D.
note:- for a subnet with n routers,the optimal number of hierarchical level is ln(n).
Now, let's solve it...
A/Q
Number of Router=400
then ,no. of optimal number of level=ln(400)
above is in to the base 'e' of the log so to convert it to base 10 we have to multiply it by 2.303 for efficient calculation.
=2.303 * log(400). [to the base 10]
=2.303 *log20²
=2.303*2log10
=2.303*2log(2*10)
=2.303*2[log2 plus log10]
=2.303*2[0.30 plus 1]
=2.303*2[1.30]
=2.303*2.60
=5.9878~6. and..