If log3 y = x and log2 z = x, then 72^x = ?

Question

If
x(x+y) = y(y+z) = z(z+x)
and
x,y,z are positive integers.
Then is it definitely true that x=y=z

Answer 1

y^2*z^3

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log3 y = x => y=3^x
log2 z = x => z=2^x
72^x = ?
72^x=(9*8)^x=(3^2*2^3)^x=(3^x)^2*(2^x)^3=y^2*z^3

Answer 2

3^x = y
2^x = z
y×z = (3^x)×(2^x)
y×z = 6^x
12×y×z = 12×6^x = 72^x