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Math Help - Are the three lines concurrent?

  1. #1
    Super Member fardeen_gen's Avatar
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    Are the three lines concurrent?







    Are the above three lines concurrent?
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    Moo
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    Hello,
    Quote Originally Posted by fardeen_gen View Post






    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 \\ \\<br />
\frac{x \ln a}{\ln b}+y+\frac{\ln c}{\ln b}=0 \\ \\<br />
\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.
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