Substitute z^x = 1000 to equation (2)

Thus,

Another way to solve for y   †

Divide equation (1) by equation (3)

Substitute y = 5/3 to z^y = 100 from above

Substitute y = 5/3 and z = 100^3/5 to equation (2)

  ‡

Thus,

  →   you can also use logarithm to solve for x from ‡ similar to solution for y in †.
 

Answer
x = 5/2
y = 5/3
z = 100^3/5