Verified answer

3^(2x)+3^(2x+1)=2*7^(2x)-5*7^(2x-1)

3^(2x-1)*(3+3^2)=7^(2x-1)*(2*7-5)

12*3^(2x-1) = 9 * 7^(2x-1)

(3/7)^(2x-1) = 9/12 = 3/4

(2x-1) log(3/4) 3/7 = 1

2x* log(3/4) 3/7 = 1 + log(3/4) 3/7

x = (1 + log(3/4) 3/7) / 2log(3/4) 3/7