Question

solve 2 to the power x + 3 to the power Y is equal to 17​

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

13p=32

p=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 both sides

x=log(189/13 base 3)

Answer 2

Answer: x=3 y=2

2^x = p

3^y = q

p + q = 17   ----- 1

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

Substitute values of 2^x and 3^y

4p - 3q = 5  ------ 2

Solve equations 1 and 2

p = 8

2^x  = 8

x = 3

Similarly,

y = 2