Given:
log a=-3
log b=-9
log c =3
To find the value of
[tex]\log \frac{a^7b^6}{c^2}[/tex]
Since, log a=-3, log b=-9, log c =3
We get,
[tex]\begin{gathered} a=e^{-3} \\ \Rightarrow a^7=e^{-21} \\ b^{}=e^{-9} \\ \Rightarrow b^6=e^{-54} \\ c=e^3 \\ \Rightarrow c^2=e^6 \end{gathered}[/tex]
Using these values in the given expression we get,
[tex]\begin{gathered} \log (\frac{e^{-21}e^{-54}}{e^6})=\log (e^{-21}^{-54-6}^{}) \\ =\log (e^{-81}) \\ =-81 \end{gathered}[/tex]
Hence, the answer is -81.
