Question

Given 32 = 2*, and 243 = 3”, then the value of (32 x 243)x-y​

Answer 1

Answer:

Given that,

3^(x - y) = 27 ….(i)

3^(x + y) = 243 ….(ii)

To solve this equations, you first need to know a law-

If a^x = a^y, then x = y.

From equation (i), we get -

3^(x - y) = 27

=> 3^(x - y) = 3^3 [From the law described above]

=> x - y = 3

=> y = x - 3 … (iii)

Now, from equation (ii), we get -

3^(x + y) = 243

=> 3^(x + y) = 243

=> 3^(x + y) = 3^5

=> x + y = 5 [From the law described above]

=> x + (x - 3) = 5 [Because, from equation (iii) y = x - 3 ]

=> x + x - 3 = 5

=> 2x - 3 = 5

=> 2x = 5 + 3

=> 2x = 8

=> x = 8/2

=> x = 4

So, x = 4

Thank you.