PART 11：例題-常用對數的計算

完成下列 \((a)(b)(c)(d)(e)\) 之值

\(\log 1=0\)

\(\log 2\doteq 0.3010\)

\(\log 3\doteq 0.4771\)

\(\log 4\doteq \underline{\ \ (a)\ \ }\)

\(\log 5\doteq \underline{\ \ (b)\ \ }\)

\(\log 6\doteq \underline{\ \ (c)\ \ }\)

\(\log 7\doteq 0.8451\)

\(\log 8\doteq \underline{\ \ (d)\ \ }\)

\(\log 9\doteq \underline{\ \ (e)\ \ }\)

\(\log 10\doteq \ \ 1\)

SOL:
利用對數律
\(\log 4=\log {{2}^{2}}=2\log 2\doteq 0.6020\cdots \cdots (a)\)
\(\log 5=\log \frac{10}{2}=\log 10-\log 2\doteq 1-0.3010=0.6990\cdots \cdots (b)\)
\(\log 6=\log 2\cdot 3=\log 2+\log 3\doteq 0.3010+0.4771=0.7781\cdots \cdots (c)\)
\(\log 8=\log {{2}^{3}}=3\log 2\doteq 0.9030\cdots \cdots (d)\)
\(\log 9=\log {{3}^{2}}=2\log 3\doteq 0.9542\cdots \cdots (e)\)