高一数学难题已知函数f(x)=log底a｜x｜(a>0,且f(x^2+4x+8)>f(-π).(1)写出函数f(x)的单

一：已知函数f(x)=log底a｜x｜(a>0,且f(x^2+4x+8)>f(-π).
(1)写出函数f(x)的单调区间,并加以证明；
(2）若方程4^a-m.2^a+1=5=0有两个不相等的实根,求m的取值
(1)解析：∵函数f(x)=log(a,|x|)(a>0, a≠1),∴其定义域为x≠0
当0-20
由换底公式得
log(a,x)+3log(a,x)/log(a,a)-log(a,y)/log(a,x)= 4log(a,x)-log(a,y)/log(a,x)=3
4[log(a,x)]^2-3 log(a,x) -log(a,y)=0
∴用loga x表示loga y
则log(a,y)＝4[log(a,x)]^2-3 log(a,x)
(2）解析：∵log(a,y)＝4[log(a,x)]^2-3 log(a,x) ＝4[log(a,x)-3/8]^2-9/16
∴当log(a,x)=3/8时,log(a,y)取最小值-9/16
∴x=a^(3/8),y取最小值a^(-9/16)