If $$2^{2x - 1} + 4^x = 3^{x - \frac{1}{2}} + 3^{x + \frac{1}{2}}$$, then x equals

Expression : $$2^{2x - 1} + 4^x = 3^{x - \frac{1}{2}} + 3^{x + \frac{1}{2}}$$

=> $$\frac{2^{2x}}{2} + 2^{2x} = \frac{3^x}{\sqrt3} + (3^x \times \sqrt3)$$

=> $$2^{2x}(\frac{1}{2}+1) = 3^x(\frac{1}{\sqrt3}+\sqrt3)$$

=> $$2^{2x}\times\frac{3}{2} = 3^x\times\frac{4}{\sqrt3}$$

=> $$2^{2x-1}\times3^1 = 3^{x-\frac{1}{2}}\times2^2$$

Now, comparing powers of (any one of) 2 or 3, we get : $$x=\frac{3}{2}$$

=> Ans - (D)