Question

If $3^{x-y}=27,3^{x+y}=243,$ what is the value of $x?$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

$3^{x-y}=27=3^3$
$\begin{array}{}\Rightarrow x-y=3& \text{(1)}\end{array}$
$3^{x+y}=243=3^5$
$\begin{array}{}\Rightarrow x+y=5& \text{(2)}\end{array}$
Solving $\left(1\right)$ and $\left(2\right)$, we get
$\therefore x=4$