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

15.9
27.7
39.5
413.1

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let 2^{3.6} \times 4^{3.6} \times 4^{3.6} \times (32)^{2.3} = {(32)}^{x} \\ Then, 2^{3.6} \times {(2^{2})}^{3.6} \times {(2^{2})}^{3.6} \times (2^{5})^{2.3} = {(2^{5})}^{x} \\ \Leftrightarrow 2^{3.6} \times 2^{(2 \times 3.6)} \times 2^{(2 \times 3.6)} \times (2^{5})^{2.3} = {(2^{5})}^{x} \\ \Leftrightarrow 2^{(3.6 + 7.2 + 7.2)} \times (2^{5})^{2.3} = {(2^{5})}^{x} \\ \Leftrightarrow 2^{18} \times (2^{5})^{2.3} = {(2^{5})}^{x} \\ \Leftrightarrow {(2^{5})}^{3.6} \times (2^{5})^{2.3} = {(2^{5})}^{x} \\ \Leftrightarrow {(2^{5})}^{(3.6 + 2.3)} = {(2^{5})}^{x} \\ \Leftrightarrow {(2^{5})}^{5.9} = {(2^{5})}^{x} \\ \Leftrightarrow x = 5.9 \end{aligned}

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