Question

If log 5 = 0.6990 then how many digits are there in 2^81

Answer 1

Answer:

24

Explanation:

2^81

=241785164*10^16

ie 8 digits + 16 digits

=24 digits

Answer 2

There are 24 digits in $2^{81}$.

Given:

log 5 = 0.6990

To find:

Number of digits in $2^{81}$.

Solution:

To find the number of digits in any number, we can find the log of the number and the integer part of what we get will be the number of digits. Therefore

$\log_{10} 2^{81} = 81\log_{10} 2$

$81\log_{10} 2 = 81 (1 - \log_{10} 5 ) = 81(1-0.6990)$

$\log_{10} 2^{81} = 24.38$

Therefore

$2^{81} = 10^{.38} * 10^{24}$

$2^{81}=2.399 * 10^{24}$

Hence the number $2^{81}$ has 24 digits.

#SPJ3