\section*{Problem 1 - 091021}

Determine the quotient \(\frac{[\lg 3790]}{[\lg 0.0379]}\) without using logarithm tables. Here, \([x]\) denotes the greatest integer that does not exceed \(x\).
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Due to \(10^{3}<3790<10^{4}\), it follows that \(3 \lg 3790<4\) and thus \([\lg 3790]=3\).

Due to \(10^{-2}<0.0379<10^{-1}\), it follows that \(-2 \lg 0.0379<-1\) and thus \([\lg 0.0379]=-2\).

Therefore, the desired quotient is \(\frac{3}{-2}=-1.5\).