given that (4radicalx)^x=x,which of the following expressions is equivalent to 4radicalx

Question

forgot how to do radicals

Answer 1

Let’s make this easier by letting y=4radicalx which I take to mean ∜x.

Now work out log(y)=log∜x to base x. This is ¼.

So we have yˣ=x.

Take logs to base x of both sides:

xlog(y)=1 so x=1/log(y)=1/¼=4.

The solution is x=4.