Logarithms

Concept:Determine the number of zeros after the decimal before the first non-zero digit using the characteristic of the logarithm.Explanation:Given $\log 3 = 0.4771$.Then $\log(3^{-20}) = -20 \times 0.4771 = -9.542$.Write $-9.542 = -10 + 0.458$, so characteristic is $-10$ and mantissa $0.458$.The number of zeros after the decimal before the first significant digit is $10 - 1 = 9$.Thus the first significant digit appears at the 10th decimal place.Answer:10th place