Cho \(\frac{{\log a}}{p} = \frac{{\log b}}{q} = \frac{{\log c}}{r} = \log x \ne 0;\frac{{{b^2}}}{{ac}} = {x^y}\). Tính \(y\) theo \(p, q, r\).

* Hướng dẫn giải

Ta có \(\frac{{{b^2}}}{{ac}} = {x^y} \Leftrightarrow \log \frac{{{b^2}}}{{ac}} = \log {x^y}\)

\(\begin{array}{l}
 \Rightarrow y\log x = 2\log b - \log a - \log c = 2q\log x - p\log x - r\log x\\
 \Rightarrow y.\log x = \left( {2q - p - r} \right).\log x\\
 \Rightarrow y = 2q - p - r\left( {\log x \ne 0} \right)
\end{array}\)