Question

find the number of digits in 4power 2013. if log2to base 10 is equal to 0.3010

Answer 1

Answer is 1212. Check the picture for the steps..

Answer 2

Answer:

he number of digits = 1212

Step-by-step explanation:

Given : If $\log _{10} 2=0.3010$

To find : The number of digits in 4 power 2013.

Solution :

Let $x=4^{2013}$

$x=2^2{^{2013}}$

$x=2^2\times{2013}$

$x=2^{4026}$

Taking log both side,

$\log x=\log 2^{4026}$

$\log x=4026\log 2$

$\log x=4026\times 0.3010$

$\log x=1211.826$

1211 is the characteristic

Number of digit  $x=4^{2013}$ is

1211+1=1212

Therefore, The number of digits = 1212