$${2^{3.6}} \times {4^{3.6}} \times {4^{3.6}} \times {(32)^{2.3}} = $$      $${\left( {32} \right)^?}$$

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let }}{2^{3.6}} \times {4^{3.6}} \times {4^{3.6}} \times {(32)^{2.3}} = {\left( {32} \right)^x} \cr & {\text{Then,}}{2^{3.6}} \times {\left( {{2^2}} \right)^{3.6}} \times {\left( {{2^2}} \right)^{3.6}} \times {({2^5})^{2.3}} = {\left( {{2^5}} \right)^x} \cr & \Leftrightarrow {2^{3.6}} \times {2^{\left( {2 \times 3.6} \right)}} \times {2^{\left( {2 \times 3.6} \right)}} \times {({2^5})^{2.3}} = {\left( {{2^5}} \right)^x} \cr & \Leftrightarrow {2^{\left( {3.6 + 7.2 + 7.2} \right)}} \times {({2^5})^{2.3}} = {\left( {{2^5}} \right)^x} \cr & \Leftrightarrow {2^{18}} \times {({2^5})^{2.3}} = {\left( {{2^5}} \right)^x} \cr & \Leftrightarrow {\left( {{2^5}} \right)^{3.6}} \times {({2^5})^{2.3}} = {\left( {{2^5}} \right)^x} \cr & \Leftrightarrow {\left( {{2^5}} \right)^{\left( {3.6 + 2.3} \right)}} = {\left( {{2^5}} \right)^x} \cr & \Leftrightarrow {\left( {{2^5}} \right)^{5.9}} = {\left( {{2^5}} \right)^x} \cr & \Leftrightarrow x = 5.9 \cr} $$