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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$20$

Vedclass · Answer

(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:

Similar Questions

$2 \log _{10} 5 + \log _{10} 8 - \frac{1}{2} \log _{10} 4 = ?$

If $y = \frac{1}{a^{1-\log _{a} x}}$,$z = \frac{1}{a^{1-\log _{a} y}}$ and $x = a^{k}$,then $k =$

If $\log _{10} 2 = 0.3010$ and $\log _{10} 7 = 0.8451,$ then the value of $\log _{10} 2.8$ is

If $\log_{10} 2 = 0.3010$,then $\log_{10}(1/2) =$

$7 \log \frac{16}{15} + 5 \log \frac{25}{24} + 3 \log \frac{81}{80} =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module