Logarithm formula proof

Prove:

$${x}^{\mathrm{log}(y)}={y}^{\mathrm{log}(x)}$$

I have been trying this for the past 1 hour, still cant prove it.

I started with

$${\mathrm{log}}_{b}(y)=m$$

$${\mathrm{log}}_{b}(x)=n$$

To show:

$${x}^{m}={y}^{n}$$

How do i proceed?

Prove:

$${x}^{\mathrm{log}(y)}={y}^{\mathrm{log}(x)}$$

I have been trying this for the past 1 hour, still cant prove it.

I started with

$${\mathrm{log}}_{b}(y)=m$$

$${\mathrm{log}}_{b}(x)=n$$

To show:

$${x}^{m}={y}^{n}$$

How do i proceed?