$6^{1.2} \times 36^{?} \times 30^{2.4} \times 25^{1.3} = 30^{5}$ ${6^{1.2}} \times {36^?} \times {30^{2.4}} \times {25^{1.3}} = {30^5}$

10.1
20.7
31.4
42.6

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let 6^{1.2} \times 36^{x} \times 30^{2.4} \times 25^{1.3} = 30^{5} \\ Then, 6^{1.2} \times (6^{2})^{x} \times (6 \times 5)^{2.4} \times (5^{2})^{1.3} = 30^{5} \\ \Leftrightarrow 6^{1.2} \times 6^{2 x} \times 6^{2.4} \times 5^{2.4} \times 5^{2.6} = (6 \times 5)^{5} \\ \Leftrightarrow 6^{(1.2 + 2 x + 2.4)} \times 5^{(2.4 + 2.6)} = 6^{5} \times 5^{5} \\ \Leftrightarrow 6^{(3.6 + 2 x)} \times 5^{5} = 6^{5} \times 5^{5} \\ \Leftrightarrow 3.6 + 2 x = 5 \\ \Leftrightarrow 2 x = 1.4 \\ \Leftrightarrow x = 0.7 \end{aligned}

$\eqalign{ & {\text{Let }}\,{6^{1.2}} \times {36^x} \times {30^{2.4}} \times {25^{1.3}} = {30^5} \cr & {\text{Then,}}\,{6^{1.2}} \times {({6^2})^x} \times {(6 \times 5)^{2.4}} \times {({5^2})^{1.3}} = {30^5} \cr & \Leftrightarrow {6^{1.2}} \times {6^{2x}} \times {6^{2.4}} \times {5^{2.4}} \times {5^{2.6}} = {(6 \times 5)^5} \cr & \Leftrightarrow {6^{\left( {1.2 + 2x + 2.4} \right)}} \times {5^{\left( {2.4 + 2.6} \right)}} = {6^5} \times {5^5} \cr & \Leftrightarrow {6^{\left( {3.6 + 2x} \right)}} \times {5^5} = {6^5} \times {5^5} \cr & \Leftrightarrow 3.6 + 2x = 5 \cr & \Leftrightarrow 2x = 1.4 \cr & \Leftrightarrow x = 0.7 \cr}$