看来√2是底.f(x)过原点,则log(√2)(0+a) = log(√2)a = 0
a = 1
f(x)有意义须x+a > 0,x+1 > 0,即x > -1,定义域为(-1,+∞).注意,不包含1
底√2＞1,所以f(x)为增函数,在[2,4]上,f(4)最大,f(2)最小.
f(4) - f(2) = log(√2)(4+a) - log(√2)(2+a) = log(√2)[(4+a)/(2+a)] = 4
(4+a)/(2+a) = (√2)^4 = 2² = 4
4+a = 8+4a
3a = -4
a = -4/3