$25^{2.7} \times 5^{4.2} \div 5^{5.4} = 25^{?}$ ${25^{2.7}} \times {5^{4.2}} \div {5^{5.4}} = {25^?}$

11.6
21.7
33.2
4None of these

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let 25^{2.7} \times 5^{4.2} \div 5^{5.4} = 25^{x} \\ Then, 25^{2.7} \times 5^{(4.2 - 5.4)} = 25^{x} \\ \Leftrightarrow 25^{2.7} \times 5^{(- 1.2)} = 25^{x} \\ \Leftrightarrow 25^{2.7} \times \frac{1}{5^{1.2}} = 25^{x} \\ \Leftrightarrow \frac{25^{2.7}}{{(5^{2})}^{0.6}} \\ \Leftrightarrow \frac{{(25)}^{2.7}}{{(25)}^{0.6}} = 25^{x} \\ \Leftrightarrow 25^{x} = 25^{(2.7 + 0.6)} = 25^{2.1} \\ \Leftrightarrow x = 2.1 \end{aligned}

$\eqalign{ & {\text{Let }}{25^{2.7}} \times {5^{4.2}} \div {5^{5.4}} = {25^x} \cr & {\text{Then, }}{25^{2.7}} \times {5^{(4.2 - 5.4)}} = {25^x} \cr & \Leftrightarrow {25^{2.7}} \times {5^{( - 1.2)}} = {25^x} \cr & \Leftrightarrow {25^{2.7}} \times \frac{1}{{{5^{1.2}}}} = {25^x} \cr & \Leftrightarrow \frac{{{{25}^{2.7}}}}{{{{\left( {{5^2}} \right)}^{0.6}}}} \cr & \Leftrightarrow \frac{{{{\left( {25} \right)}^{2.7}}}}{{{{\left( {25} \right)}^{0.6}}}} = {25^x} \cr & \Leftrightarrow {25^x} = {25^{\left( {2.7 + 0.6} \right)}} = {25^{2.1}} \cr & \Leftrightarrow x = 2.1 \cr}$