How many digits will 5^(4^(3^2)) produce?

MMDCCC50m

MMDCCC50m

Answered question

2022-11-03

How many digits will 5 4 3 2 produce?
According to Wolfram Alpha, 5 4 3 2 evaluates to an integer with 183 231 digits. How does one find out how many digits such a calculation will produce?

Answer & Explanation

hitturn35

hitturn35

Beginner2022-11-04Added 20 answers

A number n N + has log 10 n + 1 digits. For n = 5 4 3 2 , we have
log 10 5 4 3 2 = 4 9 log 10 5 = 262 144 log 10 5 183 230.8
So n has 183 231 digits.

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