# Math Help - Are the three lines concurrent?

1. ## Are the three lines concurrent?

Are the above three lines concurrent?

2. Hello,
Originally Posted by fardeen_gen

Are the above three lines concurrent?
recall the formula :
$\log_a b=\frac{\ln b}{\ln a}$ ( $a>0$ and $a \neq 1$)

So the equations are now :
$\begin{array}{lllll} x+\frac{y \ln b}{\ln a}+\frac{\ln c}{\ln a}=0 \\ \\
\frac{x \ln a}{\ln b}+y+\frac{\ln c}{\ln b}=0 \\ \\
\frac{x \ln a}{\ln c}+\frac{y \ln b}{\ln c}+1=0 \end{array}$

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.