${4^x} – {3^{x – \frac{1}{2}}} = {3^{x + \frac{1}{2}}} – {2^{2x – 1}}$ સમીકરણ આપેલ છે.

$ \Rightarrow \,\,{2^{2x}} + {2^{2x – 1}} = {3^{x + \frac{1}{2}}} + {3^{x – \frac{1}{2}}}$

$ \Rightarrow \,\,{2^{2x}}\left( {1 + \frac{1}{2}} \right) = {3^{x – \frac{1}{2}}}(1 + 3)$

$ \Rightarrow \,{2^{2x}}.\frac{3}{2} = {3^{x – \frac{1}{2}}}.4$

$ \Rightarrow \,{2^{2x – 3}} = {3^{x – \frac{3}{2}}}$

હવે  બંને બાજુ ${\rm{log }}$ લેતાં $,  \Rightarrow {\rm{ }}\,(2x – 3)\log 2 = (x – 3/2)\log 3$

$ \Rightarrow \,2x\log 2 – 3\log 2 = x\log 3 – \frac{3}{2}\log 3$

$ \Rightarrow x\log 4 – x\log 3 = 3\log 2 – \frac{3}{2}\log 3$

$ \Rightarrow \,x\log \left( {\frac{4}{3}} \right) = \log 8 – \log 3\sqrt 3 $

$ \Rightarrow \,{\left( {\frac{4}{3}} \right)^x} = \frac{8}{{3\sqrt 3 }}$

$ \Rightarrow \,{\left( {\frac{4}{3}} \right)^x} = {\left( {\frac{4}{3}} \right)^{3/2}}$

$\therefore \,\,x = \frac{3}{2}$