Question

if 4(2^x-1)+9(3^y-1)=17 and 3(2^x)-2(3^y)=6 then x+y =​

Answer 1

Answer:

4(2^x-1)+9(3^y-1)=2(2^x)+3(3^y)=17

3(2^x)-2(3^y)=6

Let 2^x=p and 3^y=q

Then two equations become

2p+3q=17 and 3p-2q=6

Now multiply 1st equation by 3 and 2nd equation by 2 then subtract 2nd equation from 1st, you will get 13q=39

q = 39/13= 3

By putting this value of q in any of the above equations you will get p=4

q=3^y=3=3^1

y=1

p=2^x=4=2^2

x=2

x+y=2+1=3 Ans