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

Question

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 (A) 3 (B) 4 (C) 5 (D) 6

Tardigrade Admin · Accepted Answer

x= operatornameantilog256(0.5)=(256)0.5=16 N=525 log N=25 log 5=17.475 y=17+1=18 M ∈[42, 43) z=43-42=64-16=48 x+2 y+z=100 34<100<35 4< log 3 100<5

Q. Let x denotes the antilog of 0.5 to the base 256 . y denotes the number of digit in 525 (Given log10​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+2y+z) to the base 3 is

3

4

5

6

x=antilog256​(0.5)=(256)0.5=16 N=525 logN=25log5=17.475 y=17+1=18 M∈[42,43) z=43−42=64−16=48 x+2y+z=100 34<100<35 4<log3​100<5

$x = antilog_{256} (0.5) = (256)^{0.5} = 16$
$N = 5^{25}$
$lo g N = 25 lo g 5 = 17.475$
$y = 17 + 1 = 18$
$M \in [4^{2}, 4^{3})$
$z = 4^{3} - 4^{2} = 64 - 16 = 48$
$x + 2 y + z = 100$
$3^{4} < 100 < 3^{5}$
$4 < lo g_{3} 100 < 5$