93指考數學乙單選第3題詳解

設實際面積比為 $k$ 倍。 感覺面積比為 $k^{0.7} = 10$。 取對數： $$0.7 \log k = 1 \implies \log k = \frac{10}{7} \approx 1.4286$$ 檢驗各選項： $(1)$ $$\log 18 = \log(2 \cdot 3^2) = 0.3010 + 2 \times 0.4771 = 1.2552$$ $(2)$ $$\log 21 = \log(3 \cdot 7) = 0.4771 + 0.8451 = 1.3222$$ $(3)$ $$\log 24 = \log(2^3 \cdot 3) = 3 \times 0.3010 + 0.4771 = 1.3801$$ $(4)$ $$\log 27 = \log(3^3) = 3 \times 0.4771 = 1.4313$$ $(5)$ $$\log 36 = \log(2^2 \cdot 3^2) = 2 \times 0.3010 + 2 \times 0.4771 = 1.5562$$ $1.4313$ 最接近 $1.4286$，故選 $(4)$。