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  • Please solve RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 9 maths textbook solution

Please solve RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 9 maths textbook solution

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Answer: x=e^{2}

Hint: Here, we use basic concept of determinant of matrix

Given: A=\left[\begin{array}{cc} \log x & -1 \\ -\log x & 2 \end{array}\right]

           det (A) = 2           

Solution: Here, A=\left[\begin{array}{cc} \log x & -1 \\ -\log x & 2 \end{array}\right]

                \begin{aligned} &|A|=\log x \times 2-(-1 \times-\log x) \\ &=2 \log x-\log x \\ &|A|=\log x \end{aligned}

\begin{aligned} &\text { And }|A|=2 \text { (Given) }\\ &\text { So, }|A|=\log x=2 \end{aligned}

                \begin{aligned} &e^{\log x}=e^{2} \\ &x=e^{2}\left[e^{\log x}=x\right] \end{aligned}

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