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Equation solver with assume

Odd behaviour: the following gives a solution:

x, c, k = var('x, c, k')
assume(k > 0)
assume(k, "integer")
solve(x**k == (k/c), x)

but the following does not:

x, c, k = var('x, c, k')
assume(k > 0)
assume(k, "real")
solve(x**k == (k/c), x)

I should be able to remove the assume(k, "datatype") completely, right?