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Q.
The number of solutions of the equation $\log _{(x-3)}\left(x^3-3 x^2-4 x+8\right)=3$ is
Continuity and Differentiability
Solution:
$ ( x -3)>0, x ^3-3 x ^2-4 x +8>0 $
$x ^3-3 x ^2-4 x +8=( x -3)^3$
$6 x ^2-31 x +35=0$
$(2 x-7)(3 x-5)=0, x=\frac{7}{2}, x=\frac{5}{3} $
$x \neq \frac{5}{3},(x-3)>0$