Logarithm calculation result I am carrying out a review of a network protocol, and the author has provided a function to calculate the average steps a message needs to take to traverse a network. 
It is written as $$\log_{2^b}(N)$$
Does the positioning of the $2^b$ pose any significance during calculation? I can't find an answer either way. The reason is, they have provided the results of their calculations and according to their paper, the result would be $1.25$ (given $b= 4$ and $N= 32$).
Another example was given this time $N= 50$, $b=4$ giving a result of $1.41$.
I don't seem to be able to get the same result if I were to apply the calculation and so it's either my method/order of working or their result is incorrect (which I doubt). 
Can someone help to provide the correct way of calculating the values, and confirm the initial results? 
My initial calculation was calculate $\log(2^4) \cdot 32$... Clearly it's totally wrong (maths is not a strong point for me). 

The base of the logarithm is $2^b$. You want to find an $x$ such that $(2^b)^x = N$, i.e. $2^{bx} = N$.
You can rewrite that as $$x = \dfrac{\log N}{b}$$ if you take the $\log$ to base-2.
