How to get a variable in a closed form given an equation

I need to express a variable in a closed form given an equation, $k^4 = 2^k.$ Taking the logarithm from both sides I get $k^{\frac{1}{k}} = 2^{\frac{1}{4}}$ which is not helping much. I tried other things but without getting a satisfactory solution. Do you have any idea how to get a closed form for $k$ ? Thanks.