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the number of digits in 2^64 is

Asked In other Harsh Poddar (9 years ago)

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Narasapu Hari prasad  (9 years ago)

ans is 20
for 2^0,2^1,2^2,2^3=single digit
for 2^4,2^5,2^6=double digit
for 2^7,2^8,2^9=triple digit
in the same way for 2^59=18 digits
for 2^60=19 digits
for 2^61 also=19 digits
for 2^62 also =19 digits
for 2^63 also =19 digits
for 2^64=20 digits

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BHASKAR MANDAL  (9 years ago)

the power of the series of 2 with the number of digits goes in the order
433 433 433......
i.e, one digit no. powers are 0,1,2,3 total 4.
from 2^0 to 2^3, 1 to 8 single digit
two digit no. powers are 4,5,6 total of 3
from 2^4 to 2^6 , 16 to 64 two digit number
and the same process continues

4,3,3, 4,3,3, 4,3,3, .......
using the above sequence we can write
power upto (4)-1 = 1 digit no.
upto power (4+3) -1 = 2 digit no.
upto power (7+3) -1 = 3 digit no.

upto power (10+4)-1 = 4 digit no.
upto power (14+3)-1 = 5 digit no.
upto power (17+3)-1 = 6 digit no.

and so on

we can see a sequence
in the power group of 10, (4+3+3) there are 3 digit changes

so 64 = 60 +4
for 10 => 3 digits
60 = > 3*6 = 18 digits
and the last 4 will contribute one more digit

so, the total number of digits will be 18+1=19

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