If `f(x)=log_(e)x and g(x)=e^(x)`, then prove that :
`f(g(x)}=g{f(x)}`

If f(x)=log_ex and g(x)=e^x , prove that f{g(x)}=g{f(x)} .

If f(x) = log x and g(x) = e^x then fog(x) is :

If f (x) = log x and g (x) = e^X , then (fog) (x) is :

Given f(x)=log_(10)x and g(x)=e^(piix) , if theta(x)=|(f(x)g(x),[ f(x)]^(g(x)),1),(f(x^(2))g(x^(2)),[f(x^(2))]^(g(x^(2))),0),(f(x^(3))g(x^(3)),[f(x^(3))]^(g(x^(3))),1)| , then the value of theta(10) is

If f(x)=e^(x) and g(x)=log_(e)x, then (gof)'(x) is

Given f(x) =log_(10) x and g(x) = e^(piix) . phi (x) =|{:(f(x).g(x),(f(x))^(g(x)),1),(f(x^(2)).g(x^(2)),(f(x^(2)))^(g(x^(2))),0),(f(x^(3)).g(x^(3)),(f(x^(3)))^(g(x^(3))),1):}| the value of phi (10), is

Given (f(x) =log_(10) x and g(x) = e^(piix) . phi (x) =|{:(f(x).g(x),(f(x))^(g(x)),1),(f(x^(2)).g(x^(2)),(f(x^(2)))^(g(x^(2))),0),(f(x^(3)).g(x^(3)),(f(x^(3)))^(g(x^(3))),1):}| the value of phi (10), is

Given (f(x) =log_(10) x and g(x) = e^(piix) . phi (x) =|{:(f(x).g(x),(f(x))^(g(x)),1),(f(x^(2)).g(x^(2)),(f(x^(2)))^(g(x^(2))),0),(f(x^(3)).g(x^(3)),(f(x^(3)))^(g(x^(3))),1):}| the value of phi (10), is

If f(x)= log_e(x+sqrt(1+x^2) , g(x)=log_e(1+sqrt(1+x^2 )and h(x)=f(x)-g(x) then prove h(1/x)=-h(x) .