If log_{10} 2 = 0.3010,the number of digits i | vedclass

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(C) To find the number of digits in $2^{64}$,we take the common logarithm (base $10$) of the number.Let $x = 2^{64}$.Taking $\log_{10}$ on both sides,

Vedclass · Accepted Answer

$20$

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(C) To find the number of digits in $2^{64}$,we take the common logarithm (base $10$) of the number.Let $x = 2^{64}$.Taking $\log_{10}$ on both sides,we get $\log_{10} x = \log_{10} (2^{64})$.Using the property $\log(a^b) = b \log a$,we have $\log_{10} x = 64 	imes \log_{10} 2$.Given $\log_{10} 2 = 0.3010$,so $\log_{10} x = 64 	imes 0.3010 = 19.264$.The number of digits in a number $x$ is given by $\lfloor \log_{10} x floor + 1$,where $\lfloor \cdot floor$ is the floor function (the characteristic of the logarithm).Here,the characteristic is $19$.Therefore,the number of digits $= 19 + 1 = 20$.

If $\log_{10} 2 = 0.3010$,the number of digits in $2^{64}$ is:

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