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Q.
The value(s) of $x$ satisfying the equation $\log x+\log (x-2)=\log \left(x^2-2 x\right)$, is
Continuity and Differentiability
Solution:
The equation is true as long as $x$ is a number that makes all three logarithms defined.
For the first one, $x>0$.
For the second one, $x>2$.
For the third one, $x<0$ or $x>2$.
$\therefore $ all three logarithms are defined for $x >2$