Question

Let $x$ denotes the antilog of 0.5 to the base 256 . $y$ denotes the number of digit in $5^{25}$ (Given ${\log }_{10}2=0.3010$ ) and $z$ denotes the number of positive integers, which have the characteristic 2 , when the base of logarithm is 4 .
$\frac{xy}{z}$ is equal to

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

Answer: (C)

$x={\mathrm{antilog}}_{256}(0.5)=(256{)}^{0.5}=16$
$N=5^{25}$
$\log N=25\log 5=17.475$
$y=17+1=18$
$M\in \left[4^2,4^3\right)$
$z=4^3-4^2=64-16=48$
$\frac{xy}{z}=\frac{16\times 18}{48}=6$