Question

To find the numerical value of the log expressionIt isLog a=-3 log b=-9 log c =3

Answer 1

Given:

log a=-3

log b=-9

log c =3

To find the value of

`\log (a^7b^6)/(c^2)`

Since, log a=-3, log b=-9, log c =3

We get,

`\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}`

Using these values in the given expression we get,

`\begin{gathered} \log ((e^(-21)e^(-54))/(e^6))=\log (e^(-21)^(-54-6)^{}) \\ =\log (e^(-81)) \\ =-81 \end{gathered}`

Hence, the answer is -81.