Dissimilar-root radical equation

Question

Sorry I wasn't able to type the equation! Here is the link and my problem is "task 15" I'll highly appreciate if you answer this question Thank you

What is the solution to the infinite equation

$\sqrt{x}\cdot\sqrt[4]{x}\cdot\sqrt[8]{x}\cdot\sqrt[16]{x}\cdot\sqrt[32]{x}\cdot\ldots=16$

Answer 1

Hint:

Consider the logarithms of both sides.

Answer 2

Well, $$ x^{1/2} \cdot x^{1/4} \cdot x^{1/8} \cdots = x^{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots} = x^1 \text{.} $$