Question

Please solve ques no. 27

Answer 1

We can write,

${2}^{x} + {3}^{y} = {2}^{3} + {3}^{2} = 8 + 9 = 17$

Hence, x = 3 and y = 2 in this case.

Now, let us try the next one;

${2}^{ x + 2} - {3}^{y + 1} = {2}^{3 + 2} - {3}^{2 + 1} = {2}^{5} - {3}^{3} = 32 - 27 = 5$

Hence, it is clear that x = 3 and y = 2.

HOPE THIS COULD HELP!!!

Answer 2

2^x + 3^y = 17 _______(1)

2^(x+2) - 3^(y+1) = 5 ______(2)

Let 2^x = a and 3^y = b then

a+b= 17 ____(1)

4a-3b = 5 ____(2)

3a + 3b = 51 ____(1)×3

4a - 3b = 5 _____(2)

adding (1)×3 and (2) we get

7a = 56

a = 8

Putting a in (1)

b = 9

Now a = 2^x

8 = 2^x

=> x = 3

also b = 3^y

9 = 3^y

=> y = 2

Hence x=3 and y=2 is the answer.