$\log_{xyz} w$

If $\log_x w = 20$ then $x^{20}= w$ .

So $y^{36} = w$ and $(xyz)^{10} = x^{10} y^{10}z^{10} = w$ .

Setting $x^{20}=y^{36}$ , we get $x^{10}=y^{18}$ .

We can set $y^{36}=x^{10}y^{10}z^{10}=y^{18}y^{10}z^{10}=y^{28}z^{10}$ .

This gives $y^{36} =y^{28}z^{10}$ .

Solving gives $y^8=z^{10}$ .

$\log_z y^8 = \log_z z^{10}$

$8log_z y^8 = 10$ $log_z y = 5/4$

Since $w=y^{36}$ , $\log_z y^{36} = 36\log_z y= 36*5/4=45$ .