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1 solution
= 3^(x-1/2) + 3^(x+1/2) = 4^(x) + 2^(2(x-1/2))
3^(x)(3^(-1/2) + 3^(1/2)) = 4^(x)(1+4^(-1/2))
3^(x)(4/3^(1/2)) = 4^(x)(3/2)
(3/4)^(x) = (3/4)^(2-1/2)
x=1.5