The value of left|begin{array}{cc}log _5 729 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the given expression be $E = D_1 	imes D_2$. First,simplify $D_1 = \left|\begin{array}{cc}\log _5 729 & \log _3 5 \ \log _5 27 & \log _9 25\

Vedclass · Accepted Answer

$(\log _3 5) 	imes (\log _5 81)$

Vedclass · Answer

(D) Let the given expression be $E = D_1 	imes D_2$. First,simplify $D_1 = \left|\begin{array}{cc}\log _5 729 & \log _3 5 \ \log _5 27 & \log _9 25\end{array}ight|$. Using $\log_a b^n = n \log_a b$ and $\log_{a^n} b = \frac{1}{n} \log_a b$: $D_1 = \left|\begin{array}{cc}6 \log _5 3 & \log _3 5 \ 3 \log _5 3 & \log _3 5\end{array}ight| = (\log _5 3)(\log _3 5) \left|\begin{array}{cc}6 & 1 \ 3 & 1\end{array}ight| = 1 	imes (6 - 3) = 3$. Next,simplify $D_2 = \left|\begin{array}{cc}\log _3 5 & \log _{27} 5 \ \log _5 9 & \log _5 9\end{array}ight|$. $D_2 = \left|\begin{array}{cc}\log _3 5 & \frac{1}{3} \log _3 5 \ 2 \log _5 3 & 2 \log _5 3\end{array}ight| = (\log _3 5)(\log _5 3) \left|\begin{array}{cc}1 & 1/3 \ 2 & 2\end{array}ight| = 1 	imes (2 - 2/3) = 4/3$. Thus,$E = 3 	imes \frac{4}{3} = 4$. Checking the options: Option $(d)$ is $(\log _3 5) 	imes (\log _5 81) = (\log _3 5) 	imes (4 \log _5 3) = 4 	imes 1 = 4$. Therefore,option $(d)$ is correct.

List-$I$	List-$II$
a) $A$ matrix which is not a square matrix	i) Symmetric matrix
b) $A$ square matrix $A' = A$	ii) Null matrix
c) The diagonal elements of a diagonal matrix are same	iii) Rectangular matrix
d) $A$ matrix which is both symmetric and skew symmetric	iv) Scalar matrix

The value of $\left|\begin{array}{cc}\log _5 729 & \log _3 5 \\ \log _5 27 & \log _9 25\end{array}\right| \times \left|\begin{array}{cc}\log _3 5 & \log _{27} 5 \\ \log _5 9 & \log _5 9\end{array}\right|$ is

Similar Questions

$\det \left[ \begin{array}{ccc} \frac{a^2+b^2}{c} & c & c \\ a & \frac{b^2+c^2}{a} & a \\ b & b & \frac{c^2+a^2}{b} \end{array} \right] = $

If $A = \begin{bmatrix} 3 & -2 \\ 4 & 2 \end{bmatrix}$, then $A^2 - 5A + 14I = 0$. Which of the following is equivalent to $A^2$?

Let $B=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]$ and $A$ be a $2 \times 2$ matrix satisfying $\left(A^T\right)^{-1}=A$. If $X=A B A^T$, then $A^T X^{2021} A=$

Let $A=\left[\begin{array}{ll}0 & 1 \\ 0 & 0\end{array}\right],$ show that $(a \mathrm{I}+b \mathrm{A})^{n}=a^{n} \mathrm{I}+n a^{n-1} b \mathrm{A},$ where $\mathrm{I}$ is the identity matrix of order $2$ and $n \in \mathrm{N}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module