Can you do it manually?

How many digits are there in 3 2 2016 32^{2016} ?


The answer is 3035.

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1 solution

Viki Zeta
Sep 13, 2016

No of digits is given by log N + 1 \log N + 1

Here N = 3 2 2016 N = 32^{2016} .

Therefore,

no of digits = ( log 3 2 2016 ) + 1 = ( 2016 log 32 ) + 1 = ( 2016 × 1.50514 ) + 1 = 3034 + 1 = 3035 (\log 32^{2016}) + 1 \\ = (2016 \log 32) + 1 \\ = (2016 \times 1.50514) + 1 \\ = 3034 + 1 = \fbox{ 3035 }

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