8. (1 mark) Given that $0.3010<\log 2<0.3011$ and $0.4771<\log 3<0.4772$. Find the leftmost digit of $12^{37}$.
(1 分) 設 $0.3010<\log 2<0.3011$ 及 $0.4771<\log 3<0.4772$, 求 $12^{37}$ 最左的一位數字。
8. Check that $\log 12=2 \log 2+\log 3$, so we have $1.0791=2 \times 0.3010+0.4771<\log 12<$ $2 \times 0.3011+0.4772=1.0794$, which implies $39+\log 8=39+3 \log 2<39.9267<37 \log 12<$ $39.9378<39+2 \log 3=39+\log 9$. Hence the leftmost digit of $12^{37}$ is $\underline{\underline{8}}$.