Reduce[ForAll[{x, y, z}, {{x, y, z} > 0, 2^x == 3^y == 5^z, #}], Reals] & /@ {2 x < 3 y < 5 z, 5 z < 2 x < 3 y, 3 y < 5 z < 2 x, 3 y < 2 x < 5 z}
Why does the result obtained using this method turn out to be incorrect?
{False, False, False, False}
