Question

Find the number of digits in 4²⁰¹³, if log₁₀2 = 0.3010.

Answer 1

$y=4^{2013} =2^{2*2013} =2^{4026}$

Take log to both sides

WE Know,

$logm^{n} =nlogm$

$logy=4026log2$

$logy=4026*(0.3010)$

              =1211.826

$y=10^{1211.826}$

       = $10^{1211}*10^{.826}$

       =6.69884609417*$10^{1211}$

Hence,no. of digits is 1212