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1. $6^{1.2} \times 36^{?} \times 30^{2.4} \times 25^{1.3} = 30^{5}$

A. 0.1

B. 0.7

C. 1.4

D. 2.6

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}

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