Cho \(a = {10^{\frac{m}{{n - \log b}}}};b = {10^{\...

B

- Hướng dẫn giải

\(\begin{array}{l}
a = {10^{\frac{m}{{n - \log b}}}} \Leftrightarrow \log a = \frac{m}{{n - \log b}}\\
 \Leftrightarrow n - \log b = \frac{m}{{\log a}}\\
 \Leftrightarrow \log b = \frac{{n\log a - m}}{{\log a}}\\
b = {10^{\frac{m}{{n - \log c}}}} \Leftrightarrow \log b = \frac{m}{{n - \log c}}
\end{array}\)

Ta có:

\(\begin{array}{l}
\log b = \frac{m}{{n - \log c}} = \frac{{n\log a - m}}{{\log a}}\\
 \Leftrightarrow n - \log c = \frac{{m\log a}}{{n\log a - m}}\\
 \Leftrightarrow \log c = \frac{{\left( {{n^2} - m} \right)\log a - mn}}{{n\log a - m}}
\end{array}\)