Question

The $3^{(x-y)}=27$ and $3^{(x+y)}=243$, then $x$ is equal to ____________.

• A. $0$
• B. $2$
• C. $4$
• D. $6$

Answer 1

Answer: (C)

$4$

Given, $3^{(x-y)}=27$ and $3^{(x+y)}=243$

We need to find value of $x$

We know $3^{(x-y)}=3^3$

$\Rightarrow x-y=3$ .....(1)

And $3^{(x+y)}=2^5$

$\Rightarrow x+y=5$ ....(2)

Solving (1) and (2), we get

$x=4,y=1$

Thus value of $x$ is $4$.