Question

2 power x + 3 power Y is equals to 17 2 X + 2 - 3 power Y + 1 is equals to 5

Answer 1

Step-by-step explanation:

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

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

2^2× 2^x - 3^y/3 = 5

4.2^x - 3^y/3 = 5                                                                   -----------(2)

Let 2^x = P

3^y = Q

so,

P + Q = 17

4P -Q/3 = 5

12P - Q = 15

solve both equation ,

P + Q + 12P - Q = 17 + 15

13 P = 32

P = 32/13

2^x = 32/13

take log both sides

x log2 = log32/13

x = log( 32/13 base 2)

Q = 17 -32/13 = (221-32)/13 = 189/13

3^x = 189/13

take log both sides

x = log ( 189/13 base 3)

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