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Log zero is not defined, and if it were defined, it would be more likely to be minus infinity than infinity.
Yes they are most likely used in your everyday life- even if you don't realize it. Computers use prime numbers in the encryption techniques. If you log in to a website in secure mode, most likely prime numbers are being used, but you don't even know about it.
This goes way beyond the capabilities of most scientific calculators! You can calculate this with logarithms. I'll use base-10 logarithms. Call the result "x": x = 26972593 log x = log 26972593 log x = 6972593 log 2 log x = 6972593 times 0.30103 log x = 2099000 Now take antilogarithms: x = 102099000