Question

please solve this it's urgent ​

Answer 1

Step-by-step explanation:

$\color{magenta} \text{We have, \( \tt 3^{x+y}=81 \)}$

$\color{red}\[ \begin{array}{l} \tt \Longrightarrow 3^{x+y}=3^{4} \\ \\ \tt \Longrightarrow x+y=4 \qquad \cdots(i)\left[\text { If } \tt a^{m}=a^{n}\right. \text { then } \tt m=n] \end{array} \]$

$\color{olive}\[ \begin{array}{l} \text { and } \\ \tt 81^{x-y}=3 \\ \\ \tt \Longrightarrow\left(3^{4}\right)^{x-y}=3^{1} \\ \\ \tt\Longrightarrow 3^{4 x-4 y}=3^{1} \\ \\ \tt\Longrightarrow 4 x-4 y=1 \qquad \cdots(i i) \end{array} \]$

Multiplying (i) by 4 , we get $\tt 4 x+4 y=16 \cdots(i i i)$

Adding (ii) and (iii), we get $8 x=17$ $\tt\Longrightarrow x=\frac{17}{8}$

Substituting $\tt x=\frac{17}{8}$ in (i) , we get

hence correct option is (c).