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Question: \[\left| \begin{matrix} 1 & 5 & \pi \\ \log_{e}e & 5 & \sqrt{5} \\ \log_{10}10 & 5 & e \end{matrix} ...

1 & 5 & \pi \\ \log_{e}e & 5 & \sqrt{5} \\ \log_{10}10 & 5 & e \end{matrix} \right| =$$
A

π\sqrt{\pi}

B

e

C

1

D

0

Answer

0

Explanation

Solution

Δ=∣15π15515e∣=0\Delta = \left| \begin{matrix} 1 & 5 & \pi \\ 1 & 5 & \sqrt{5} \\ 1 & 5 & e \end{matrix} \right| = 0 (∵log⁡aa=1 and 5C1≡C2)(\because\log_{a}a = 1\text{ and }5C_{1} \equiv C_{2})