9^x-2^(x+1/2)=2^(x+7/2)-3^(2x-1
3^2x+3^2x*1/3=2^x*2^7/2+2^x*2^1/2
9^x(1+1/3)=2^x(2^1/2(2^3+1)
9^x/2^x=9*2^1/2/(4/3)
(9/2)^x=27*(2^(1/2-2))
(9/2)^x=(9^3/2)/2^3/2
(9/2)^x=(9/2)^3/2
x=3/2
x=1.5
9^x-2^(x+1/2)=2^(x+7/2)-3^(2x-1
3^2x+3^2x*1/3=2^x*2^7/2+2^x*2^1/2
9^x(1+1/3)=2^x(2^1/2(2^3+1)
9^x/2^x=9*2^1/2/(4/3)
(9/2)^x=27*(2^(1/2-2))
(9/2)^x=(9^3/2)/2^3/2
(9/2)^x=(9/2)^3/2
x=3/2
x=1.5