已知lgM lgN=21g(M-2N),求log根2 M/N
2个回答

lgM + lgN = lg (MN)

2 lg(M-2N) = lg (M-2N)²

∵lgM + lgN = 2 lg(M-2N)

∴ MN = (M-2N)²

MN = M² - 4MN + 4N²

M²- 5MN +N² = 0

同除以 N²

(M/N)² - 5M/N + 4 = 0

(M/N - 1)(M/N - 4) = 0

M/N = 1 或 M/N = 4

又 M - 2N > 0 (真数大于0)

M/N > 2

∴ M/N = 4

log √2 (M/N) = log√2 (4) = log√2 [(√2)⁴] = 4