#### Answer

$x = \frac{6}{5}$ (Correct answer)
Marie subtracted $x$ from $5x^{2}$, which is wrong. She should have divided $5x^{2}$ by $x$ instead of subtracting.

#### Work Step by Step

Marie subtracted $x$ from $5x^{2}$, which is wrong. She should have divided $5x^{2}$ by $x$ instead of subtracting.
$\log_6 (5x^{2}) - \log_6 x = 1$
$\log_6 \frac{5x^{2}}{x} = 1$
$\log_6 5x = 1$
$6 = 5x$
$x = \frac{6}{5}$