for the first one, raise everything to the power of e:

e^(ln(x^2*z^3/y)) = e

e^(ln(x^4*y/z)) = e^2

e^(ln(y^3 * z^5/x^2)) = e^3

this reduces down to:

x^2*z^3/y = e

x^4*y/z = e^2

y^3 * z^5/x^2 = e^3

From here, solve like a normal system of equations system.

The same goes for the second set, except take the natural log of everything. This works because:

e^(ln(x)) = x

ln(e^x) = x