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Q.
The number of value(s) of $x$ satisfying the equation
$
4^{\log _2(\ln x)}-1+\ln ^3 x-3 \ln ^2 x-5 \ln x+7=0
$
Continuity and Differentiability
Solution:
$ (\ln x)^2-1+(\ln x-1)\left(\ln ^2 x -2 \ln x -7\right)=0$
$(\ln x -1)\left[(\ln x +1)+\left(\ln ^2 x -2 \ln x -7\right)\right]=0$
$\therefore \ln x =1 ; \ln x =-2 ; \ln x =3 $
But $\ln x =1 $ & $\ln x =3 \text { are acceptable only } $
$\therefore x = e$ & $x = e ^3 $