Cho các số thực x, y, z thỏa mãn y = 10^(1/1-logx) , z =10^(1/(1-logy

* Hướng dẫn giải

Đáp án D

Ta có

$$\begin{gathered} \left\{\begin{array}{l}y={10}^{\frac{1}{1-\log \text{x}}}\\ z={10}^{\frac{1}{1-\log \text{y}}}\end{array}\right.\iff \left\{\begin{array}{l}\log y=\frac{1}{1-\log \text{x}}\\ \log z=\frac{1}{1-\log \text{y}}\end{array}\right. \\ \iff \left\{\begin{array}{l}\log y=\frac{1}{1-\log \text{z}}\\ \log y=\frac{1}{1-\log \text{x}}\end{array}\right.\Rightarrow 1-\frac{1}{1-\log \text{z}}=\frac{1}{1-\log \text{x}} \\ \iff \frac{\log \text{z}-1}{\log \text{z}}=\frac{1}{1-\log \text{x}}\iff 1-\log \text{x}=\frac{\log \text{z}}{\log \text{z}-1} \\ \iff \log \text{x}=-\frac{1}{\log \text{z}-1}\iff x={10}^{\frac{1}{1-\log \text{z}}} \end{gathered}$$