Where is my mistake in a logarithm?

Question

Prove that

$$3^{\log_2 5} = 5^{\log_2 3}$$

is true.

Here is my solution:

Answer 1

The easiest way to do this is just to take $\log_2$ of both sides.

---

In the picture I see an expression which looks like $3^X=0$. But there isn't a real number $X$ for which this is true. You would need the expression to be equal to $1$ for the exponent to be zero.

Answer 2

$$ 3^{\log(5)}=5^{\log(3)} \iff\log(3^{\log(5)})=\log(5^{\log(3)}) \iff \log(3)\log(5)=\log(3)\log(5)$$