Thank you for reporting, we will resolve it shortly
Q.
If $\log _2\left(9^{x-1}+7\right)-\log _2\left(3^{x-1}+1\right)=2$, then the sum of value(s) of $x$ is equal to
Continuity and Differentiability
Solution:
$\log _2\left(\frac{9^{x-1}+7}{3^{x-1}+1}\right)=2$
$\frac{\left(3^{ x -1}\right)^2+7}{3^{ x -1}+1}=4 \text { Put } 3^{ x -1}= t $
$t ^2+7=4 t +4 \Rightarrow t ^2-4 t +3=0 \Rightarrow( t -1)( t -3)=0 $
$t =1 \Rightarrow 3^{ x -1}=1 \Rightarrow x -1=0 \Rightarrow x =1 $
$t =3 \Rightarrow 3^{ x -1}=3 \Rightarrow x -1=1 \Rightarrow x =2$