In chapter 10.6.1 in Nielsen and Chuang, the section on concatenated codes and the threshold theorem (pages 480-481) states:
The size of the simulating circuit goes as $d^k$ times the size of the original circuit, where $d$ is a constant representing the maximum number of operations used in a fault-tolerant procedure to do an encoded gate and error correction.
It is further explained that if we wish to achieve a final accuracy of $\epsilon$, we are required to concatenate the simulating circuit $k$ times such that:
$$ \frac{(cp)^{2^k}}{c} \leq \frac{\epsilon}{p(n)} \tag{10.113} $$
where $p(n)$ is the number of gates in the simulating circuit and $\frac{(cp)^{2^k}}{c}$ is the failure probability for a procedure at the highest level.
After this, the size of the circuit is to achieve this accuracy is then given as:
$$ d^k = \left(\frac{\log{(p(n)/c\epsilon)}}{\log(1/pc)}\right)^{\log{d}} \tag{10.114} $$
My question is, how is the size of the circuit derived in Eq(10.114)? It is closely related to Eq(10.113) after some rearranging, but I cannot see exactly how to get Eq(10.114).