f(3^x)=4xlog2(3)+233
=log2[2^233*(3^x)4]
令t=3^x
f(t)=log2(t^4)+233
即f(x)的函数表达式为:
f(x)=log2(x^4)+233
f(2)+f(4)+...+f(2^8)
=233*8+log2[2^(1+2+...+8)]^4
=1864+log2[2^(8*9/2)]^4
=1864+log2(2^144)
=1864+144
=2008