I think it would be two solutions
Each octave in the piano is composed of 8 keys with the end key overlapping the next one which means the last key is the first key of the next octave. In 52 white keys, there are 7 octaves which is composed of 43 full keys and 7 overlapping keys. Answer to this problem is 7 octaves.
the base must be raised
for example
55 = n ( the base is 10 ), then
55 = ![10^{n}](https://tex.z-dn.net/?f=10%5E%7Bn%7D)