Hello,
recall the formula :
$\displaystyle \log_a b=\frac{\ln b}{\ln a}$ ($\displaystyle a>0$ and $\displaystyle a \neq 1$)
So the equations are now :
$\displaystyle \begin{array}{lllll} x+\frac{y \ln b}{\ln a}+\frac{\ln c}{\ln a}=0 \\ \\
\frac{x \ln a}{\ln b}+y+\frac{\ln c}{\ln b}=0 \\ \\
\frac{x \ln a}{\ln c}+\frac{y \ln b}{\ln c}+1=0 \end{array}$
Multiply the first one by ln(a), the second one by ln(b), the third one by ln(c) and you'll see that they're identical. So the lines are the same.