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