2log_{2}(x-1)-log_{2}(4-x)=2

解答

2 lo g_{2} (x - 1) - lo g_{2} (4 - x) = 2

x = 3

求解步骤

2 lo g_{2} (x - 1) - lo g_{2} (4 - x) = 2

使用对数运算法则

(x - 1)^{2} = 4 (4 - x)

解

(x - 1)^{2} = 4 (4 - x) : x = 3, x = - 5

x = 3, x = - 5

验证解:

x = 3

真

, x = - 5

假

解是

x = 3

(lo g_{10} (x^{2}))^{2} = 1

ln (x + 2) = ln (12) - ln (x + 3)

lo g_{10} (C) = 10

lo g_{10} (x) = - lo g_{10} (ab)

lo g_{2} (\frac{x}{10000}) = 50