Rewrite using one log:

Undo.

Solve for $x$.

$\text{log}_3\frac{x+2}{x}=2$

$\small 3^{\text{log}_{3}\frac{x+2}{x}}=3^2$

$\frac{x+2}{x}=9$

$x+2=9x$

$2 = 8x$

$x = \frac{1}{4}$

1. Divide both sides by $50$.
2. Take the log of both sides bring the exponent down.
3. Solve for $x$.