For a growing quantity to reach a value 32 times its initial value, how many doubling times are required?

The doubling time would be in an exponential expression, that is:

x^y

where x is the quantity being doubled, and y is the doubling times

Since it must be equal to 32 times the initial value, therefore:

x^y = 32 x

x^y / x = 32

x^ (y - 1) = 32

(y - 1) log x = log 32

y = (log32 / log x) + 1

x is the initial value, y is the doubling required