The Greek God Zeus ordered his blacksmith Hephaestus to create a perpetual water-making machine to fill Zeus' mighty chalice. The volume of Zeus' chalice was reported to hold about one hundred and fifty sextillion gallons (that is a fifteen followed by twenty-two zeros). If Hephaetus' machine pours out 2 gallon in the first minute and then doubles its output each minute, find in which minute would this hypothetical machine pour out a single quantity of water that would be enough to fill Zeus' chalice with water?

To solve this problem, we need to determine the number of minutes it would take for the machine to pour out a quantity of water that would be enough to fill Zeus' chalice.

We know that the machine pours out 2 gallons in the first minute and then doubles its output each subsequent minute.

Let's look at the output of the machine for the first few minutes:
- 1st minute: 2 gallons
- 2nd minute: 2 * 2 = 4 gallons
- 3rd minute: 2 * 2 * 2 = 8 gallons
- 4th minute: 2 * 2 * 2 * 2 = 16 gallons
- 5th minute: 2 * 2 * 2 * 2 * 2 = 32 gallons

From the pattern, we can see that the output of the machine doubles with each minute. So, the formula for the output of the machine in the nth minute would be 2^n.

Now, we need to determine the minute at which the output of the machine would be enough to fill Zeus' chalice.

To do that, we need to solve the equation 2^n = 150 sextillion gallons.

Taking the logarithm of both sides of the equation, we get:
log(2^n) = log(150 sextillion)

Using the logarithmic property log(a^b) = b * log(a), we can simplify this to:
n * log(2) = log(150 sextillion)

Solving for n, we get:
n = log(150 sextillion) / log(2)

Calculating this using a calculator, we find that n is approximately equal to 53.165.

Since the number of minutes must be a whole number, we can round up to the nearest whole number. Therefore, the machine would pour out a single quantity of water that would be enough to fill Zeus' chalice in the 54th minute.