\section*{Problem 1 - 031031}

Solve the equation \(\lg (2 x+1)-\lg x=2\).
}

Using the laws of logarithms and the fact that \(\lg x=2\) only holds for \(x=100\), it follows:

\[
\begin{array}{r}
\lg (2 x+1)-\lg x=\lg \frac{2 x+1}{x}=2 \\
\frac{2 x+1}{x}=100 \Rightarrow x=\frac{1}{98}
\end{array}
\]