Answer
$x=\dfrac{2}{35}$
Work Step by Step
Apply the quotient rule to have:
$\log_6{\left(\frac{x+2}{x}\right)}=2$
RECALL:
$\log_a{b}=x \longrightarrow a^x=b $
where $b\gt0$
Use this rule in converting the equation to its equivalent exponential equation to have:
$6^2=\dfrac{x+2}{x}
\\36=\dfrac{x+2}{x}
\\36(x)=x+2
\\36x=x+2
\\36x-x=2
\\35x=2
\\x=\dfrac{2}{35}$
