Question

If f(x) = `"log"_("x"^2) ("log x")`, then f(e) is ____________.

Options

• 0

• 1

• `1/"e"`

• `1/(2"e")`

Answer 1

If f(x) = `"log"_("x"^2) ("log x")`, then f(e) is `underline(1/(2"e"))`.

Explanation:

as f(x) `= "log" ("log x")/(2 "log x")`

`=> "f'"("x") = 1/2 [(("log x". 1/"log x". 1/x - "log" ("log x"). 1/"x")/("log x")^2]`

`=> "f'"("x") = 1/2 [(1 - "log" ("log x"))/("x" ("log x")^2)]`

`=> "f'"("e") = 1/2 [(1 - "log" ("log e"))/("e"("log e")^2)] = 1/(2"e")`