Question

Solve the pair of equations:
2^x+3^y=17;
2^x+2-3^y-1=5

Answer 1

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)

Answer 2

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