Question

How do you solve $\log \left(\frac{1}{x}\right)=7.761$?

Answer 1

Solve for $x$ using the given relation:

Assume that the logarithm has base 10, since no base is given

$$\begin{gathered} {\log }_{10}\left(\frac{1}{x}\right)=7.761 \\ \Rightarrow \left(\frac{1}{x}\right)={10}^{7.761} \\ \Rightarrow x=\frac{1}{{10}^{7.761}} \\ \Rightarrow x={10}^{-7.761} \end{gathered}$$ $\left[\because {\log }_a\left(b\right)=x\Rightarrow b=a^x\right]$

Hence the answer is ${10}^{-7.761}$.