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Expanding Huge Numbers To Exponents Of Base 10:
E.g. Number Of DNA Base Pair Combinations With 1,000,000 Base Pairs:
4^1,000,000. The resulting number is multiplied by 10 to the nth power.
In this simplified example, the nth power will be 602,059: 10^602,059.
10^602,059 is an enormous number of combinations with 602,059 zeros.
This simplified logarithm calculation gives you the exponent of base 10.
Converting base 4 with high exponents to base 10:

Internet Exponent Page      My Logarithm Calculations  

4^100 = 10^60      log4 x 100 = 10^60.205
4^1,000 = 10^602       log4 x 1,000 = 10^602.059
4^10,000 = 10^6,020       log4 x 10,000 = 10^6,020.599
4^100,000 = 10^60,205       log4 x 100,000 = 10^60,205.999
4^1,000,000 = 10^602,000       log4 x 1,000,000 = 10^602,059.991

Using my Sharp Scientific Calculator: 4^100 = 1.6 x 10^60 [Won't Display 4^1,000]

According to Wikipedia, standard QR codes can contain up to 23,624 bits. There can also be different densities in codes. Each bit has 2 states so the number of possible permutations is 2^23624 or about 3.4 x 10^7111, an absolutely enormous number. Using logarithms, this is approximately 23624 X log 2 = 23624 X 3.01029995 = 7111.5326. The number to left of decimal is called the "characteristic" of logarithm and indicates that base 10 is raised to to the power of 7111 (10^7111)! The number to right of decimal is the "mantissa" of logarithm. On another Internet site they are using 23648 bits and 5.719 x 10^7118. Using logarithms this would be 23648 x log2 = 7118.757 and the power of base 10 comes out to 10^7118. The power of base 10 is what makes these numbers almost infinite. The purpose of this page was to show how to calculate the exponent of base 10. This is also why over 7,000 zeros must be added to the number. When you consider that 10^80 is the number of electrons in some models of our visible universe, these numbers for possible DNA arrangements and QR codes are astronomical.

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