$3^{x - y} = 27$ and $3^{x + y} = 243$ , then $x$ is equal to

0

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4

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2

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6

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Solution

The correct option is A $4$
Make the bases of the sides of each equation same. Apply the concept if $a^{m} = a^{n} t h e n m = n$ .

$3^{x - y} = 27 = 3^{3}$

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

And, $3^{x + y} = 243 = 3^{5}$

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

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

We get, $x = 4, y = 1$

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