Q59 / 160 · TS EAMCET 2006 · Mathematics

$\left|\begin{array}{ccc} \log e & \log e^2 & \log e^3 \\ \log e^2 & \log e^3 & \log e^4 \\ \log e^3 & \log e^4 & \log e^5 \end{array}\right| \text { is equal to : }$

  • Correct answer
    A
    0
  • B
    1
  • C
    $4 \log e$
  • D
    $5 \log e$

Solution

$\left|\begin{array}{ccc}\log e & \log e^2 & \log e^3 \\ \log e^2 & \log e^3 & \log e^4 \\ \log e^3 & \log e^4 & \log e^5\end{array}\right|$ $=\left|\begin{array}{ccc}\log e & 2 \log e & 3 \log e \\ 2 \log e & 3 \log e & 4 \log e \\ 3 \log e & 4 \log e & 5 \log e\end{array}\right|$ $=\left|\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5\end{array}\right|$ $=\left|\begin{array}{lll|l}1 & 1 & 1 \\ 2 & 1 & 1 \\ 3 & 1 & 1\end{array}\right| C_2 \rightarrow C_2-C_1$ $=0 \quad(\because$ Two columns are identical $)$

Hence, the correct answer is option: 'A'.

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