Question

The value(s) of $x$ satisfying the equation $\log x+\log (x-2)=\log \left(x^2-2x\right)$, is

• A. $x<0$
• B. $x>2$
• C. $0<x<2$
• D. all real numbers

Answer 1

Answer: (B)

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 $x>2$