(7/9)^x=7^(1-x)

take log of both sides :

x log(7/9) = (1-x) log(7)

=> x[ log(7) - log(9)] = log(7) - x log(7)

=> xlog(7) - xlog(9) = log(7) - xlog(7)

=> 2xlog(7) -x log(9) = log(7)

=> 2x (0.845098) - x(0.954243) = 0.845098

=> x(2*0.845098 - 0.954243) = 0.845098

=> x(0.735954) = 0.845098

=> x = 0.845098 /0.735954

=> x = 1.148303

You can check the answer by substituting the value of x.

I hope it helps.