已知 $2^x=3^y=5^z > 1$, 则
$ \text{A.} $ $2 x < 3 y < 5 z$ $ \text{B.} $ $5 z < 2 x < 3 y$ $ \text{C.} $ $3 y < 5 z < 2 x$ $ \text{D.} $ $3 y < 2 x < 5 z$
【答案】 D

【解析】 $\left(2^x\right)^{30}=\left(3^y\right)^{30}=\left(5^z\right)^{30} \cdot \Rightarrow\left(2^{15}\right)^{2 x}=\left(3^{10}\right)^{3 y}=\left(5^6\right)^{5 z}$.
$$
\begin{aligned}
& \left(2^x\right)^{30}=\left(3^y\right)^{30}=\left(5^z\right)^{30} . \Rightarrow\left(2^{15}\right)^{2 x}=\left(3^{10}\right)^{3 y}=\left(5^6\right)^{5 z} . \\
& \because 25 < 32,8 < 9 . \quad \therefore 5^6 < 2^{15} < 3^{10} . \quad \therefore 2 x < 3 y < 5 .
\end{aligned}
$$
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