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Q.
If $N =\left(\log _2 125+1\right)\left(2+\log _4 625\right)-\left(\log _2 25\right)\left(\log _4(15625)+4\right)$ then $N$ is equal to
Continuity and Differentiability
Solution:
$N =\left(3 \log _2 5+1\right)\left(2+2 \log _2 5\right)-\left(2 \log _2 5\right) \times\left(3 \log _2 5+4\right)$
$\text { Let } \log _2 5= t $
$N =(3 t +1)(2+2 t )-(2 t )(3 t +4)$
$N =6 t ^2+8 t +2-6 t ^2-8 t =2$
$\therefore N =2$