1. Tardigrade
  2. Question
  3. Mathematics
  4. Let x denotes the antilog of 0.5 to the base 256 . y denotes the number of digit in 525 (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 . Characteristic of number (x+2 y+z) to the base 3 is

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Q. 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 .
Characteristic of number $(x+2 y+z)$ to the base 3 is

Continuity and Differentiability

Solution:

$ x=\operatorname{antilog}_{256}(0.5)=(256)^{0.5}=16$
$N=5^{25} $
$\log N=25 \log 5=17.475$
$y=17+1=18$
$M \in\left[4^2, 4^3\right)$
$z=4^3-4^2=64-16=48$
$x+2 y+z=100 $
$3^4<100<3^5 $
$4<\log _3 100<5$