Is there any x?

Algebra Level 2

If $x^4=2^x$ & $x$ is a natural number find $x$ .

8 12 16 28 4

1 solution

A Former Brilliant Member
Sep 27, 2019

The equation indicates that $x$ must be a power of $2$ . It's an easy check that $x=2^4=16$

It's easy to check that this is an answer, but can we prove that it is the only one?

Mike Harding - 1 year, 8 months ago

In fact, if x is a real number, there are actually three different values for x: x≈1.23963, x≈-0.861345, x=16.

If x is a complex number, there exist another two values: x≈-0.160887+0.959105i, x≈-0.160887-0.959105i.

Alice Smith - 1 year, 8 months ago

That’s cool. I guess one could approximate the real number solutions by graphing, but how did you calculate the real & complex values?

Richard Costen - 1 year, 8 months ago

@Richard Costen – Well, by using Wolfram Mathematica.

Alice Smith - 1 year, 8 months ago