### 2 (two)

The equation 2^{x} = *x*^{2} can be solved by thinking carefully.

##### Solution 1

For *x* = 2 you can see immediately that it is correct, because

2

^{2}= 2^{2}⇒ 4 = 4 ⇒ 0 = 0

##### Solution 2

Also *x* = 4 is a solution that you can guess quite easily, because

2

^{4}= 4^{2}⇒ 16 = 16 ⇒ 0 = 0

##### Solution 3

If you draw a graph you see that there are three intersection points.

With a bit of dexterity, you can find the value *x* = −0.7667… on a calculator, because

2

^{−0,7667}= (−0,7667)^{2}⇒ 0,587... = 0,587... ⇒ 0 = 0

where this answer is accurate to three decimal places.

##### Further explanation

Let's do something different, and take *x*→∞. Then you can write

That seems like a good answer, but something's not right here, because

∞ − ∞ = ?

Infinity is not a number with a specific value. So there remain three solutions.