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Câu hỏi: Cho $\log 3=m;\ln 3=n$. Hãy biểu diễn $\ln 30$ theo m và n.
A. $\ln 30=\dfrac{n}{m}+1$
B. $\ln 30=\dfrac{m}{n}+n$
C. $\ln 30=\dfrac{n+m}{n}$
D. $\ln 30=\dfrac{n}{m}+n$
A. $\ln 30=\dfrac{n}{m}+1$
B. $\ln 30=\dfrac{m}{n}+n$
C. $\ln 30=\dfrac{n+m}{n}$
D. $\ln 30=\dfrac{n}{m}+n$
Ta có $\left\{ \begin{aligned}
& \log 3=m \\
& \ln 3=n \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& 3={{10}^{m}} \\
& 3={{e}^{n}} \\
\end{aligned} \right.\Rightarrow {{10}^{n}}={{e}^{n}}\Leftrightarrow n=m\ln 10\Leftrightarrow \ln 10=\dfrac{n}{m}$.
Vậy $\ln 30=\ln 3+\ln 10=n+\dfrac{n}{m}$.
& \log 3=m \\
& \ln 3=n \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& 3={{10}^{m}} \\
& 3={{e}^{n}} \\
\end{aligned} \right.\Rightarrow {{10}^{n}}={{e}^{n}}\Leftrightarrow n=m\ln 10\Leftrightarrow \ln 10=\dfrac{n}{m}$.
Vậy $\ln 30=\ln 3+\ln 10=n+\dfrac{n}{m}$.
Đáp án D.