若整数a.b.c满足20/3的a次方乘以8/15的b次方乘以9/16的c次方等于4,求a.b.c拜托各位了 3Q

(20/3)^a*(8/15)^b*(9/16)^c=4 4^a*5^a/3^a*8^b/(3^b*5^b)*9^c/16^c=4 2^2a*2^3b/2^4c*5^a/5^b*3^2c/(3^a*3^b)=4 2^(2a+3b-4c)*5^(a-b)*3^2c-a-b)=2^2 2a+3b-4c=2 a-b=0 2c-a-b=0 a=b=c=2