If N =( log 2 125+1)(2+ log 4 625)-( log 2 25)( log 4(15625)+4) then N is equal to

Question

If N =( log 2 125+1)(2+ log 4 625)-( log 2 25)( log 4(15625)+4) then N is equal to (A) prime number (B) irrational number (C) rational number which is not natural number (D) natural number which is coprime with 5

Tardigrade Admin · Accepted Answer

N =(3 log 2 5+1)(2+2 log 2 5)-(2 log 2 5) ×(3 log 2 5+4) text Let log 2 5= t N =(3 t +1)(2+2 t )-(2 t )(3 t +4) N =6 t 2+8 t +2-6 t 2-8 t =2 ∴ N =2

Q. If $N = (lo g_{2} 125 + 1) (2 + lo g_{4} 625) - (lo g_{2} 25) (lo g_{4} (15625) + 4)$ then $N$ is equal to

prime number

irrational number

rational number which is not natural number

natural number which is coprime with 5

$N = (3 lo g_{2} 5 + 1) (2 + 2 lo g_{2} 5) - (2 lo g_{2} 5) \times (3 lo g_{2} 5 + 4)$
$Let lo g_{2} 5 = t$
$N = (3 t + 1) (2 + 2 t) - (2 t) (3 t + 4)$
$N = 6 t^{2} + 8 t + 2 - 6 t^{2} - 8 t = 2$
$∴ N = 2$

Q. If N=(log2​125+1)(2+log4​625)−(log2​25)(log4​(15625)+4) then N is equal to