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109學測數學考科-11


<多選題>設a,b,c為實數且滿足\(\log a = 1.1\)、\(\log b = 2.2\)、\(\log c = 3.3\)。試選出正確的選項。
(1) \( a + c = 2b \)
(2) \( 1 \lt a \lt 10 \)
(3) \( 1000 \lt c \lt 2000 \)
(4) \( b = 2a \)
(5) \( a, b, c \) 成等比數列。

答案

\(a = 10^{1.1}\), \(b = 10^{2.2} = a^2\), \(c = 10^{3.3} = a^3\),故a,b,c成等比。估算得 \(10 \lt a \lt 20\), \(1000 \lt c \lt 2000\),故選(3)(5)。 報錯
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