I´ve been struggling with this problem too. Essentialiy we have to prove that the second expression in the min expression

.
is a valid

as explains magdon in
Quote:
Originally Posted by magdon
Rather than solve the inequality in (b) to get this bound, you may rather just verify that this is a bound by showing that if  , then the inequality in (b) is satisfied, namely  .
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this means that the inequality
![(d_{VC}+K)^{7(d_{VC}+K)} > 2K\left[7(d_{VC}+K)\log_2(d_{VC}K)\right]^{d_{VC}} (d_{VC}+K)^{7(d_{VC}+K)} > 2K\left[7(d_{VC}+K)\log_2(d_{VC}K)\right]^{d_{VC}}](/vblatex/img/0627a1ffcda472949bf578cae6a0bb29-1.gif)
(1)
must be satisfied.
I have been finding upper bounds to the right hand side of (1), using the following tricks

if

(the case

must be proved apart).

,

, because

(this is not the seven in the exponent) and

.
Then we arrive at an expression that can be compared easily with the left hand side of (1) proving that this inequality is valid.