Question

Решите систему уравнений:

2^x*3^y=108;

3^x*2^y=72.

Answer 1

 

$2^x*3^y=108\ 3^x*2^y=72\ (2^x*3^y)=108 = 2*2*3*3*3\ (3^x*2^y) = 72 = 2*2*2*3*3\ 2^{x-2}*3^{y-3}=1\ 3^{x-2}*2^{y-3}=1\ x - 2 = 0\ y - 3 = 0\ x = 2\ y = 3$