Question

If $3^{x-y}=27$ and $3^{x+y}=243$, find the value of $x$.

• A. $0$
• B. $2$
• C. $4$
• D. $6$

Answer 1

Answer: (C)

$4$

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

$3^{x-y}=3^3$

$3^{x+y}=3^5$

As bases are equal powers must be equal

$x-y=3$ and $x+y=5$

Adding them,

$x-y+x+y=8$

$2x=8$

$x=4$

Thus, $4-y=3$

$y=1$