[m](0,4^2)^{x+\frac{1}{2}}=\frac{2\cdot 2^{\frac{1}{2}}\cdot 5^{\frac{1}{2}}}{5^2}[/m]
[m](0,4)^{2\cdot (x+\frac{1}{2})}=\frac{ 2^{1+\frac{1}{2}}}{5^{2-\frac{1}{2}}}[/m]
[m](\frac{2}{5})^{2x+1} =(\frac{2}{5})^{\frac{3}{2}}[/m]
[m]2x+1=\frac{3}{2}[/m]
[m]x=\frac{1}{4}[/m]