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Câu hỏi: Cho $a=\log 5, b=\ln 5$, hệ thức nào sau đây là đúng?
A. $10e={{5}^{\dfrac{1}{a}+\dfrac{1}{b}}}$.
B. $\dfrac{a}{b}=\dfrac{e}{10}$.
C. ${{a}^{10}}={{e}^{b}}$.
D. ${{a}^{10+b}}={{5}^{10e}}$.
$\left\{ \begin{aligned}
& a=\log 5 \\
& b=\ln 5 \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& \dfrac{1}{a}={{\log }_{5}}10 \\
& \dfrac{1}{b}={{\log }_{5}}e \\
\end{aligned} \right.\Rightarrow \dfrac{1}{a}+\dfrac{1}{b}={{\log }_{5}}\left( 10e \right)$.
Do đó: $10e={{5}^{\dfrac{1}{a}+\dfrac{1}{b}}}$.
A. $10e={{5}^{\dfrac{1}{a}+\dfrac{1}{b}}}$.
B. $\dfrac{a}{b}=\dfrac{e}{10}$.
C. ${{a}^{10}}={{e}^{b}}$.
D. ${{a}^{10+b}}={{5}^{10e}}$.
$\left\{ \begin{aligned}
& a=\log 5 \\
& b=\ln 5 \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& \dfrac{1}{a}={{\log }_{5}}10 \\
& \dfrac{1}{b}={{\log }_{5}}e \\
\end{aligned} \right.\Rightarrow \dfrac{1}{a}+\dfrac{1}{b}={{\log }_{5}}\left( 10e \right)$.
Do đó: $10e={{5}^{\dfrac{1}{a}+\dfrac{1}{b}}}$.
Đáp án A.