Is there an easy way to calculate antilogarithms?

Your answer tells me that you don’t actually understand antilogs.
This is ok, it is complicated stuff.

However; the answer to this is easy.
It is a one with 37 zeros or:

10,000,000,000,000,000,000,000,000,000,000,000

I explain how to mentally calculate the first 21numbers here:

So for 37, just extrapolate.

However; again I think you want to know something else.

The antilog of a number is the base number to the power of the number.
So assuming base 10, the antilog of 37 is 10^{37}.

You now have the links how to calculate both log and antilogs.
You can apply this to calculate log 37 .

Hint: since 37 is prime, I would take the middle of log 36 and log 38.
Then use 36 = 6*6 and 38 = 19*2.