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

Answer: (D)

$4$

$3^{x-y}=27=3^3$........(1)

And $3^{x+y}=243=3^5$........(2)

Multiply both the equations

$\Rightarrow 3^{x+y}\cdot 3^{x-y}=3^3\cdot 3^5$

$\Rightarrow 3^{x+y+x-y}=3^{3+5}=3^8$

$\Rightarrow 3^{2x}=3^8$

$\Rightarrow 2x=8$ .................. Equate exponents

$\Rightarrow x=4$