求使方程log(√a)(x - a) = log(a)(x^2 + a^2 - 4)有解的实数a的取值范围.
1、作为被开平方数,应该为非复数,即a≥0
2、作为对数的底数,应该大于零,且不等于1,即a＞0,a≠1
3、log(√a)(x - a) = log(a)(x^2 + a^2 - 4)
log(a)(x - a)/log(a)√a = log(a)(x^2 + a^2 - 4)
2log(a)(x - a) = log(a)(x^2 + a^2 - 4)
(x - a)^2 = x^2 + a^2 - 4
x^2 - 2ax + a^2 = x^2 + a^2 - 4
-2ax = -4
a = 2/x(由于a＞0,且a≠1,故x＞0)
综合1、2、3的结果,求得实数a的取值范围是:a＞0,且a≠1.