sqrt((2008))(x)^(log_(2008)x)=x^(2)

x^(2009) xx(1)/(x^(2008))=x

log_(sqrt(2))sqrt(x)+log_(2)x log_(4)(x^(2))+log_(8)(x^(3))+log_(16)(x^(4))=40 then x is equal to

sqrt(5-log_(2)x)=3-log_(2)x

Let f(x)=(2007^(x))/(2007^(x)+sqrt(2007)) Then find the value of quad 2007^(x)+sqrt(2007)(1)/(2)+f((2)/(2008))+f((3)/(2008))+...+f((2007)/(2008))

Let f(x)=((2008)^(x)+(2008)^(-x))/(2),g(x)=((2008)^(x)-(2008)^(-x))/(2) then prove that f(x+y)=f(x)f(y)+g(x)g(y)

((x-4)^(2005)dot(x+8)^(2008)(x+1))/(x^(2006)(x-2)^3dot(x+3)^5 0(x-6)(x+9)^(2010))lt=0

((x-4)^(2005)*(x+8)^(2008)*(x+1))/(x^(2006)(x-2)^(3)(x+3)^(5)*(x-6)(x+9)^(2010))<0

((x-4)^(2005)*(x+8)^(2008)(x+1))/(x^(2006)(x-2)^(3)*(x+3)^(5)0(x-6)(x+9)^(2010))<=0

sqrt(log_(2)(2x^(2))log_(4)(16x))=log_(4)x^(3)