質問: log7 (7 + x2 + 2x) then which of the following is true. given log10 (6) ≈ 0.77, log10 (5) ≈ 0.69"
回答: "calculation: log5 (6) = log10 (6)log10 (5) ⇒ 1 < log5 6 < 2 ⇒ 1 < log7 (7 + x2 + 2x) < 2 (∵ log5 6 = log7 (7 + x2 + 2x)) ⇒ 7 < 6 + (1 + x2 + 2x) < 49 ⇒ 1 < (x + 1)2 < 43 ⇒ 1 < x + 1 < √43 ⇒ 0 < x < (√43 – 1) ∴ 0 < x < (√43 – 1) is true additional information log5 (6) = log10 (6)log10 (5) ⇒ log10 (6)log10 (5) ≈ 1.11 ⇒ 1"